Extended multiple transform selection for video coding

ABSTRACT

An example device for coding video data includes a memory configured to store video data; and one or more processors implemented in circuitry and configured to: code a first codeword representing a selected transform scheme of a set of transform candidates of a multiple transform selection (MTS) scheme for a current block of video data, the selected transform scheme being a secondary transform of a set of available secondary transforms to be applied in addition to a primary transform; code a second codeword representing the secondary transform from the set of available secondary transforms; and apply the primary transform and the secondary transform during coding of residual data for the current block. The second codeword may be a value for a low-frequency non-separable transform (LFNST) syntax element.

This application is a continuation of U.S. application Ser. No.16/838,553, filed Apr. 2, 2020, which claims the benefit of U.S.Provisional Application No. 62/830,125, filed Apr. 5, 2019, and U.S.Provisional Application No. 62/855,398, filed May 31, 2019, the entirecontents of each of which are hereby incorporated by reference.

TECHNICAL FIELD

This disclosure relates to video coding, including video encoding andvideo decoding.

BACKGROUND

Digital video capabilities can be incorporated into a wide range ofdevices, including digital televisions, digital direct broadcastsystems, wireless broadcast systems, personal digital assistants (PDAs),laptop or desktop computers, tablet computers, e-book readers, digitalcameras, digital recording devices, digital media players, video gamingdevices, video game consoles, cellular or satellite radio telephones,so-called “smart phones,” video teleconferencing devices, videostreaming devices, and the like. Digital video devices implement videocoding techniques, such as those described in the standards defined byMPEG-2, MPEG-4, ITU-T H.263, ITU-T H.264/MPEG-4, Part 10, Advanced VideoCoding (AVC), the High Efficiency Video Coding (HEVC) standard, ITU-TH.265/High Efficiency Video Coding (HEVC), and extensions of suchstandards. The video devices may transmit, receive, encode, decode,and/or store digital video information more efficiently by implementingsuch video coding techniques.

Video coding techniques include spatial (intra-picture) predictionand/or temporal (inter-picture) prediction to reduce or removeredundancy inherent in video sequences. For block-based video coding, avideo slice (e.g., a video picture or a portion of a video picture) maybe partitioned into video blocks, which may also be referred to ascoding tree units (CTUs), coding units (CUs) and/or coding nodes. Videoblocks in an intra-coded (I) slice of a picture are encoded usingspatial prediction with respect to reference samples in neighboringblocks in the same picture. Video blocks in an inter-coded (P or B)slice of a picture may use spatial prediction with respect to referencesamples in neighboring blocks in the same picture or temporal predictionwith respect to reference samples in other reference pictures. Picturesmay be referred to as frames, and reference pictures may be referred toas reference frames.

SUMMARY

In general, this disclosure describes techniques related to transformcoding in video coding. Transform coding is an important element ofmodem video compression standards. This disclosure describes multipletransform selection (MTS) designs that extend other MTS tools, such asthose of Versatile Video Coding (VVC)/ITU-T H.266. Since the designsdescribed in this disclosure allow an encoder to choose a transform frommore transform candidates, these techniques can improve codingefficiency. This disclosure also describes various simplified versionsof Low-Frequency Non-separable Transformation (LFNST) that can reduceencoder and decoder complexity without significant degradation in codingefficiency. Thus, these techniques may be used in advanced video codecsand next generation video coding standards, such as VVC.

In one example, a method of coding (encoding or decoding) video dataincludes coding a first codeword representing a selected transformscheme of a set of transform candidates of a multiple transformselection (MTS) scheme for a current block of video data, the selectedtransform scheme being a secondary transform of a set of availablesecondary transforms to be applied in addition to a primary transform;coding a second codeword representing the secondary transform from theset of available secondary transforms; and applying the primarytransform and the secondary transform during coding of residual data forthe current block.

In another example, a device for coding video data includes a memoryconfigured to store video data; and one or more processors implementedin circuitry and configured to: code a first codeword representing aselected transform scheme of a set of transform candidates of a multipletransform selection (MTS) scheme for a current block of video data, theselected transform scheme being a secondary transform of a set ofavailable secondary transforms to be applied in addition to a primarytransform; code a second codeword representing the secondary transformfrom the set of available secondary transforms; and apply the primarytransform and the secondary transform during coding of residual data forthe current block.

In another example, a device for coding video data includes means forcoding a first codeword representing a selected transform scheme of aset of transform candidates of a multiple transform selection (MTS)scheme for a current block of video data, the selected transform schemebeing a secondary transform of a set of available secondary transformsto be applied in addition to a primary transform; means for coding asecond codeword representing the secondary transform from the set ofavailable secondary transforms; and means for applying the primarytransform and the secondary transform during coding of residual data forthe current block.

In another example, a computer-readable storage medium has storedthereon instructions that, when executed, cause a processor to code afirst codeword representing a selected transform scheme of a set oftransform candidates of a multiple transform selection (MTS) scheme fora current block of video data, the selected transform scheme being asecondary transform of a set of available secondary transforms to beapplied in addition to a primary transform; code a second codewordrepresenting the secondary transform from the set of available secondarytransforms; and apply the primary transform and the secondary transformduring coding of residual data for the current block.

The details of one or more examples are set forth in the accompanyingdrawings and the description below. Other features, objects, andadvantages will be apparent from the description and drawings, and fromthe claims.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram illustrating an example video encoding anddecoding system that may perform the techniques of this disclosure.

FIGS. 2A and 2B are conceptual diagrams illustrating an example quadtreebinary tree (QTBT) structure, and a corresponding coding tree unit(CTU).

FIGS. 3A and 3B are conceptual diagrams illustrating an exampletransform scheme based on a residual quadtree of High Efficiency VideoCoding (HEVC).

FIG. 4 is a block diagram illustrating an example system for hybridvideo encoding with adaptive transform selection.

FIGS. 5A and 5B are conceptual diagrams illustrating horizontal andvertical transforms as a separate transform implementation.

FIG. 6 is a conceptual diagram representing an example of multipletransform selection (MTS) signaling used to identify two transforms.

FIG. 7 is a conceptual diagram illustrating an example transformassignment and corresponding unary codewords.

FIG. 8 is a conceptual diagram illustrating an example MTS designsupporting secondary transforms.

FIG. 9 is a conceptual diagram illustrating examples of low-frequencynon-separable transforms (LFNST) that a video coder (video encoder orvideo decoder) may apply.

FIG. 10 is a conceptual diagram illustrating an example of an LFNSTapplied to a subset of coefficients (at the top-left part) of an H×Wblock.

FIGS. 11A and 11B are conceptual diagrams illustrating an exampletwo-step LFNST process implementation.

FIG. 12 is a block diagram illustrating an example video encoder thatmay perform the techniques of this disclosure.

FIG. 13 is a block diagram illustrating an example video decoder thatmay perform the techniques of this disclosure.

FIG. 14 is a flowchart illustrating an example method for encoding acurrent block according to the techniques of this disclosure.

FIG. 15 is a flowchart illustrating an example method for decoding acurrent block of video data according to the techniques of thisdisclosure.

FIG. 16 is a flowchart illustrating an example video encoding method inaccordance with the techniques of this disclosure.

FIG. 17 is a flowchart illustrating an example video decoding method inaccordance with the techniques of this disclosure.

DETAILED DESCRIPTION

This disclosure describes techniques related to transform coding, whichis an important element of modern video compression standards, e.g., asdiscussed in M. Wien, High Efficiency Video Coding: Coding Tools andSpecification, Springer-Verlag, Berlin, 2015. This disclosure describesextended multiple transform selection (MTS) techniques.

In general, video data is represented as a sequential series ofpictures. A video coder partitions the pictures into blocks, and codeseach of the blocks. Coding generally includes prediction and residualcoding. During prediction, the video coder may form a prediction blockusing intra-prediction (in which the prediction block is formed fromneighboring, previously coded blocks of the same picture) orinter-prediction (in which the prediction block is formed frompreviously coded blocks of previously coded pictures). A residual blockrepresents pixel-by-pixel differences between the prediction block andan original, uncoded block. A video encoder may apply a transform to theresidual block to produce a transform block including transformcoefficients, whereas a video decoder may apply an inverse transform tothe transform block to reproduce a version of the residual block.

Assume an input N-point vector is denoted as x=[x₀, x₁, . . . ,x_(N−1)]^(T), and it is transformed to another N-point transformcoefficient vector denoted as y=[y₀, y₁, . . . , y_(N−1)]^(T) bymultiplying a matrix, the process of which can be further illustratedaccording to one of the following transform formulation, wherein kranges from 0 through N−1, inclusive:

DCT Type-I (DCT-1):

$\mspace{20mu}{{y_{k} = {\sum\limits_{n = 0}^{N - 1}{\sqrt{\frac{2}{N - 1}}{{\cos\left( \frac{\pi \cdot n \cdot k}{N - 1} \right)} \cdot w_{0} \cdot w_{1} \cdot x_{n}}}}},{{{where}\mspace{14mu} w_{0}} = \left\{ {\begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} n} = {{0\mspace{14mu}{or}\mspace{14mu} n} = {N - 1}}} \\{1,} & {otherwise}\end{matrix},{w_{1} = \left\{ \begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} k} = {{0\mspace{14mu}{or}\mspace{14mu} k} = {N - 1}}} \\{1,} & {otherwise}\end{matrix} \right.}} \right.}}$

DCT Type-II (DCT-2):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N}}{{\cos\left( \frac{\pi \cdot \left( {n + 0.5} \right) \cdot k}{N - 1} \right)} \cdot w_{0} \cdot x_{n}}}}},{{{where}\mspace{14mu} w_{0}} = \left\{ \begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} k} = 0} \\{1,} & {otheriwse}\end{matrix} \right.}$

DCT Type-III (DCT-3):

$y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N}}{{\cos\left( \frac{\pi \cdot n \cdot \left( {k + 0.5} \right)}{N} \right)} \cdot w_{0} \cdot x_{k}}}}$${{where}\mspace{14mu} w_{0}} = \left\{ \begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} k} = 0} \\{1,} & {otheriwse}\end{matrix} \right.$

DCT Type-IV (DCT-4):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N}}{{\cos\left( \frac{\pi \cdot \left( {n + 0.5} \right) \cdot \left( {k + 0.5} \right)}{N} \right)} \cdot x_{n}}}}},$

DCT Type-V (DCT-5):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N - 0.5}}{{\cos\left( \frac{\pi \cdot n \cdot k}{N - 0.5} \right)} \cdot w_{0} \cdot w_{1} \cdot x_{n}}}}},{{{where}\mspace{14mu} w_{0}} = \left\{ {\begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} n} = 0} \\{1,} & {otheriwse}\end{matrix},{w_{1} = \left\{ \begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} k} = 0} \\{1,} & {otheriwse}\end{matrix} \right.}} \right.}$

DCT Type-VI (DCT-6):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N - 0.5}}{{\cos\left( \frac{\pi \cdot \left( {n + 0.5} \right) \cdot k}{N - 0.5} \right)} \cdot w_{0} \cdot w_{1} \cdot x_{n}}}}},{{{where}\mspace{14mu} w_{0}} = \left\{ {\begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} n} = {N - 1}} \\{1,} & {otheriwse}\end{matrix},{w_{1} = \left\{ \begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} k} = 0} \\{1,} & {otheriwse}\end{matrix} \right.}} \right.}$

DCT Type-VII (DCT-7):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N - 0.5}}{{\cos\left( \frac{\pi \cdot n \cdot \left( {k + 0.5} \right)}{N - 0.5} \right)} \cdot w_{0} \cdot w_{1} \cdot x_{n}}}}},{{{where}\mspace{14mu} w_{0}} = \left\{ {\begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} n} = 0} \\{1,} & {otheriwse}\end{matrix},{w_{1} = \left\{ \begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} k} = {N - 1}} \\{1,} & {otheriwse}\end{matrix} \right.}} \right.}$

DCT Type-VIII (DCT-8):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N + 0.5}}{{\cos\left( \frac{\pi \cdot \left( {n + 0.5} \right) \cdot \left( {k + 0.5} \right)}{N + 0.5} \right)} \cdot x_{n}}}}},$

DST Type-I (DST-1):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N + 1}}{{\sin\left( \frac{\pi \cdot \left( {n + 1} \right) \cdot \left( {k + 1} \right)}{N + 1} \right)} \cdot x_{n}}}}},$

DST Type-II (DST-2):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N}}{{\sin\left( \frac{\pi \cdot \left( {n + 0.5} \right) \cdot \left( {k + 1} \right)}{N} \right)} \cdot w_{0} \cdot x_{n}}}}},{{{where}\mspace{14mu} w_{0}} = \left\{ \begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} k} = {N - 1}} \\{1,} & {otheriwse}\end{matrix} \right.}$

DST Type-III (DST-3):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N}}{{\sin\left( \frac{\pi \cdot \left( {n + 1} \right) \cdot \left( {k + 0.5} \right)}{N} \right)} \cdot w_{0} \cdot x_{n}}}}},{{{where}\mspace{14mu} w_{0}} = \left\{ \begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} n} = {N - 1}} \\{1,} & {otheriwse}\end{matrix} \right.}$

DST Type-IV (DST-4):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N}}{{\sin\left( \frac{\pi \cdot \left( {n + 0.5} \right) \cdot \left( {k + 0.5} \right)}{N} \right)} \cdot x_{n}}}}},$

DST Type-V (DST-5):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N + 0.5}}{{\sin\left( \frac{\pi \cdot \left( {n + 1} \right) \cdot \left( {k + 1} \right)}{N + 0.5} \right)} \cdot x_{n}}}}},$

DST Type-VI (DST-6):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N + 0.5}}{{\sin\left( \frac{\pi \cdot \left( {n + 0.5} \right) \cdot \left( {k + 1} \right)}{N + 0.5} \right)} \cdot x_{n}}}}},$

DST Type-VII (DST-7):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N + 0.5}}{{\sin\left( \frac{\pi \cdot \left( {n + 1} \right) \cdot \left( {k + 0.5} \right)}{N + 0.5} \right)} \cdot x_{n}}}}},$

DST Type-VIII (DST-8):

${y_{k} = {\sum\limits_{n = 0}^{N - 1}\;{\sqrt{\frac{2}{N - 0.5}}{{\cos\left( \frac{\pi \cdot \left( {n + 0.5} \right) \cdot \left( {k + 0.5} \right)}{N - 0.5} \right)} \cdot w_{0} \cdot w_{1} \cdot x_{n}}}}},{{{where}\mspace{14mu} w_{0}} = \left\{ {\begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} n} = {N - 1}} \\{1,} & {otheriwse}\end{matrix},{w_{1} = \left\{ \begin{matrix}{\frac{1}{\sqrt{2}},} & {{{if}\mspace{14mu} k} = {N - 1}} \\{1,} & {otheriwse}\end{matrix} \right.}} \right.}$

The transform type is specified by the mathematical formulation of thetransform basis function. For example, 4-point DST-VII and 8-pointDST-VII have the same transform type, regardless the value of N.

Without loss of generality, all the above transform types can berepresented using the below generalized formulation:y _(m)=Σ_(n=0) ^(N−1) T _(m,n) ·x _(n),where T is the transform matrix specified by the definition of onecertain transform, e.g., DCT Type-I˜DCT Type-VIII, or DST Type-I˜DSTType-VIII, and the row vectors of T, e.g., [T_(i,0), T_(i,1), T_(i,2), .. . T_(i,N−1)] are the i^(th) transform basis vectors. A transformapplied on the N-point input vector is called an N-point transform.

It is also noted that the above transform formulations, which areapplied on the 1-D input data x, can be represented in matrixmultiplication form as belowy=T·xwhere T indicates the transform matrix, x indicates the input datavector, and y indicates the output transform coefficients vector.

The transforms as introduced above are applied on 1-D input data, andtransforms can be also extended for 2-D input data sources. Supposing Xis an input M×N data array. The typical methods of applying transform on2-D input data include separable and non-separable 2-D transforms.

A separable 2-D transform applies 1-D transforms for the horizontal andvertical vectors of X sequentially, formulated as below:Y=C·X·R ^(T)where C and R denote the given M×M and N×N transform matrices,respectively. From the formulation, it can be seen that C applies 1-Dtransforms for the column vectors of X, while R applies 1-D transformsfor the row vectors of X. In the later part of this disclosure, forsimplicity, C and R can denote left (vertical) and right (horizontal)transforms and can be considered to form a transform pair. There arecases when C is equal to R and is an orthogonal matrix. In such a case,the separable 2-D transform is determined by just one transform matrix.

A non-separable 2-D transform first reorganized all the elements of Xinto a single vector, namely X′, by doing the following mathematicalmapping as an example:X′ _((i·N+j)) =X _(i,j)

Then a 1-D transform T′ is applied for X′ as below:Y=T′·Xwhere T′ is an (M*N)×(M*N) transform matrix.

In video coding, separable 2-D transforms are generally applied, becauseseparable 2-D transforms typically require fewer operation (addition andmultiplication) counts compared to 1-D transforms.

In conventional video codecs, such as H.264/AVC, an integerapproximation of the 4-point and 8-point Discrete Cosine Transform (DCT)Type-II is always applied for both Intra and Inter prediction residual.To better accommodate the various statistics of residual samples, moreflexible types of transforms other than DCT Type-II are utilized in thenew generation video codec. For example, in HEVC, an integerapproximation of the 4-point Type-VII Discrete Sine Transform (DST) isutilized for Intra prediction residual, which is both theoreticallyproven and experimentally validated (in J. Han, A. Saxena and K. Rose,“Towards jointly optimal spatial prediction and adaptive transform invideo/image coding,” IEEE International Conference on Acoustics, Speechand Signal Processing (ICASSP), March 2010, pp. 726-729) that DSTType-VII is more efficient than DCT Type-II for residuals vectorsgenerated along the Intra prediction directions. For example, DSTType-VII is more efficient than DCT Type-II for row residual vectorsgenerated by the horizontal Intra prediction direction. In HEVC, aninteger approximation of 4-point DST Type-VII is applied only for 4×4luma Intra prediction residual blocks. The 4-point DST-VII used in HEVCis shown below,

-   -   4×4 DST-VII:    -   {29, 55, 74, 84}    -   {74, 74, 0,−74}    -   {84,−29,−74, 55}    -   {55,−84, 74,−29}

In HEVC, for residual blocks that are not 4×4 luma Intra predictionresidual blocks, integer approximations of the 4-point, 8-point,16-point and 32-point DCT Type-II are also applied, as shown below:

-   -   4-point DCT-II:    -   {64, 64, 64, 64}    -   {83, 36,−36,−83}    -   {64,−64,−64, 64}    -   {36,−83, 83,−36}    -   8-point DCT-II:    -   {64, 64, 64, 64, 64, 64, 64, 64}    -   {89, 75, 50, 18,−18,−50,−75,−89}    -   {83, 36,−36,−83,−83,−36, 36, 83}    -   {75,−18,−89,−50, 50, 89, 18,−75}    -   {64,−64,−64, 64, 64,−64,−64, 64}    -   {50,−89, 18, 75,−75,−18, 89,−50}    -   {36,−83, 83,−36,−36, 83,−83, 36}    -   {18,−50, 75,−89, 89,−75, 50,−18}    -   16-point DCT-II:    -   {64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64}    -   {90, 87, 80, 70, 57, 43, 25, 9, −9,−25,−43,−57,−70,−80,−87,−90}    -   {89, 75, 50, 18,−18,−50,−75,−89,−89,−75,−50,−18, 18, 50, 75, 89}    -   {87, 57, 9,−43,−80,−90,−70,−25, 25, 70, 90, 80, 43, −9,−57,−87}    -   {83, 36,−36,−83,−83,−36, 36, 83, 83, 36,−36,−83,−83,−36, 36, 83}    -   {80, 9,−70,−87,−25, 57, 90, 43,−43,−90,−57, 25, 87, 70, −9,−80}    -   {75,−18,−89,−50, 50, 89, 18,−75,−75, 18, 89, 50,−50,−89,−18, 75}    -   {70,−43,−87, 9, 90, 25,−80,−57, 57, 80,−25,−90, −9, 87, 43,−70}    -   {64,−64,−64, 64, 64,−64,−64, 64, 64,−64,−64, 64, 64,−64,−64, 64}    -   {57,−80,−25, 90, −9,−87, 43, 70,−70,−43, 87, 9,−90, 25, 80,−57}    -   {50,−89, 18, 75,−75,−18, 89,−50,−50, 89,−18,−75, 75, 18,−89, 50}    -   {43,−90, 57, 25,−87, 70, 9,−80, 80, −9,−70, 87,−25,−57, 90,−43}    -   {36,−83, 83,−36,−36, 83,−83, 36, 36,−83, 83,−36,−36, 83,−83, 36}    -   {25,−70, 90,−80, 43, 9,−57, 87,−87, 57, −9,−43, 80,−90, 70,−25}    -   {18,−50, 75,−89, 89,−75, 50,−18,−18, 50,−75, 89,−89, 75,−50, 18}    -   {9, −25, 43,−57, 70,−80, 87,−90, 90,−87, 80,−70, 57,−43, 25, −9}    -   32-point DCT-II:    -   {64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64}    -   {90,90,88,85,82,78,73,67,61,54,46,38,31,22,13,4,−4,−13,−22,−31,−38,−46,−54,−61,−67,−73,−78,−82,−85,−88,−90,−90}    -   {90,87,80,70,57,43,25,9,−9,−25,−43,−57,−70,−80,−87,−90,−90,−87,−80,−70,−57,−43,−25,−9,9,25,43,57,70,80,87,90}    -   {90,82,67,46,22,−4,−31,−54,−73,−85,−90,−88,−78,−61,−38,−13,13,38,61,78,88,90,85,73,54,31,4,−22,−46,−67,−82,−90}    -   {89,75,50,18,−18,−50,−75,−89,−89,−75,−50,−18,18,50,75,89,89,75,50,18,−18,−50,−75,−89,−89,−75,−50,−18,18,50,75,89}    -   {88,67,31,−13,−54,−82,−90,−78,−46,−4,38,73,90,85,61,22,−22,−61,−85,−90,−73,−38,4,46,78,90,82,54,13,−31,−67,−88}    -   {87,57,9,−43,−80,−90,−70,−25,25,70,90,80,43,−9,−57,−87,−87,−57,−9,43,80,90,70,25,−25,−70,−90,−80,−43,9,57,87}    -   {85,46,−13,−67,−90,−73,−22,38,82,88,54,−4,−61,−90,−78,−31,31,78,90,61,4,−54,−88,−82,−38,22,73,90,67,13,−46,−85}    -   {83,36,−36,−83,−83,−36,36,83,83,36,−36,−83,−83,−36,36,83,83,36,−36,−83,−83,−36,36,83,83,36,−36,−83,−83,−36,36,83}    -   {82,22,−54,−90,−61,13,78,85,31,−46,−90,−67,4,73,88,38,−38,−88,−73,−4,67,90,46,−31,−85,−78,−13,61,90,54,−22,−82}    -   {80,9,−70,−87,−25,57,90,43,−43,−90,−57,25,87,70,−9,−80,−80,−9,70,87,25,−57,−90,−43,43,90,57,−25,−87,−70,9,80}    -   {78,−4,−82,−73,13,85,67,−22,−88,−61,31,90,54,−38,−90,−46,46,90,38,−54,−90,−31,61,88,22,−67,−85,−13,73,82,4,−78}    -   {75,−18,−89,−50,50,89,18,−75,−75,18,89,50,−50,−89,−18,75,75,−18,−89,−50,50,89,18,−75,−75,18,89,50,−50,−89,−18,75}    -   {73,−31,−90,−22,78,67,−38,−90,−13,82,61,−46,−88,−4,85,54,−54,−85,4,88,46,−61,−82,13,90,38,−67,−78,22,90,31,−73}    -   {70,−43,−87,9,90,25,−80,−57,57,80,−25,−90,−9,87,43,−70,−70,43,87,−9,−90,−25,80,57,−57,−80,25,90,9,−87,−43,70}    -   {67,−54,−78,38,85,−22,−90,4,90,13,−88,−31,82,46,−73,−61,61,73,−46,−82,31,88,−13,−90,−4,90,22,−85,−38,78,54,−67}    -   {64,−64,−64,64,64,−64,−64,64,64,−64,−64,64,64,−64,−64,64,64,−64,−64,64,64,−64,−64,64,64,−64,−64,64,64,−64,−64,64}    -   {61,−73,−46,82,31,−88,−13,90,−4,−90,22,85,−38,−78,54,67,−67,−54,78,38,−85,−22,90,4,−90,13,88,−31,−82,46,73,−61}    -   {57,−80,−25,90,−9,−87,43,70,−70,−43,87,9,−90,25,80,−57,−57,80,25,−90,9,87,−43,−70,70,43,−87,−9,90,−25,−80,57}    -   {54,−85,−4,88,−46,−61,82,13,−90,38,67,−78,−22,90,−31,−73,73,31,−90,22,78,−67,−38,90,−13,−82,61,46,−88,4,85,−54}    -   {50,−89,18,75,−75,−18,89,−50,−50,89,−18,−75,75,18,−89,50,50,−89,18,75,−75,−18,89,−50,−50,89,−18,−75,75,18,−89,50}    -   {46,−90,38,54,−90,31,61,−88,22,67,−85,13,73,−82,4,78,−78,−4,82,−73,−13,85,−67,−22,88,−61,−31,90,−54,−38,90,−46}    -   {43,−90,57,25,−87,70,9,−80,80,−9,−70,87,−25,−57,90,−43,−43,90,−57,−25,87,−70,−9,80,−80,9,70,−87,25,57,−90,43}    -   {38,−88,73,−4,−67,90,−46,−31,85,−78,13,61,−90,54,22,−82,82,−22,−54,90,−61,−13,78,−85,31,46,−90,67,4,−73,88,−38}    -   {36,−83,83,−36,−36,83,−83,36,36,−83,83,−36,−36,83,−83,36,36,−83,83,−36,−36,83,−83,36,36,−83,83,−36,−36,83,−83,36}    -   {31,−78,90,−61,4,54,−88,82,−38,−22,73,−90,67,−13,−46,85,−85,46,13,−67,90,−73,22,38,−82,88,−54,−4,61,−90,78,−31}    -   {25,−70,90,−80,43,9,−57,87,−87,57,−9,−43,80,−90,70,−25,−25,70,−90,80,−43,−9,57,−87,87,−57,9,43,−80,90,−70,25}    -   {22,−61,85,−90,73,−38,−4,46,−78,90,−82,54,−13,−31,67,−88,88,−67,31,13,−54,82,−90,78,−46,4,38,−73,90,−85,61,−22}    -   {18,−50,75,−89,89,−75,50,−18,−18,50,−75,89,−89,75,−50,18,18,−50,75,−89,89,−75,50,−18,−18,50,−75,89,−89,75,−50,18}    -   {13,−38,61,−78,88,−90,85,−73,54,−31,4,22,−46,67,−82,90,−90,82,−67,46,−22,−4,31,−54,73,−85,90,−88,78,−61,38,−13}    -   {9,−25,43,−57,70,−80,87,−90,90,−87,80,−70,57,−43,25,−9,−9,25,−43,57,−70,80,−87,90,−90,87,−80,70,−57,43,−25,9}    -   {4,−13,22,−31,38,−46,54,−61,67,−73,78,−82,85,−88,90,−90,90,−90,88,−85,82,−78,73,−67,61,−54,46,−38,31,−22,13,−4}

FIG. 1 is a block diagram illustrating an example video encoding anddecoding system 100 that may perform the techniques of this disclosure.The techniques of this disclosure are generally directed to coding(encoding and/or decoding) video data. In general, video data includesany data for processing a video. Thus, video data may include raw,uncoded video, encoded video, decoded (e.g., reconstructed) video, andvideo metadata, such as signaling data.

As shown in FIG. 1 , system 100 includes a source device 102 thatprovides encoded video data to be decoded and displayed by a destinationdevice 116, in this example. In particular, source device 102 providesthe video data to destination device 116 via a computer-readable medium110. Source device 102 and destination device 116 may comprise any of awide range of devices, including desktop computers, notebook (i.e.,laptop) computers, tablet computers, set-top boxes, telephone handsetssuch smartphones, televisions, cameras, display devices, digital mediaplayers, video gaming consoles, video streaming device, or the like. Insome cases, source device 102 and destination device 116 may be equippedfor wireless communication, and thus may be referred to as wirelesscommunication devices.

In the example of FIG. 1 , source device 102 includes video source 104,memory 106, video encoder 200, and output interface 108. Destinationdevice 116 includes input interface 122, video decoder 300, memory 120,and display device 118. In accordance with this disclosure, videoencoder 200 of source device 102 and video decoder 300 of destinationdevice 116 may be configured to apply the techniques for coding MTSdata. Thus, source device 102 represents an example of a video encodingdevice, while destination device 116 represents an example of a videodecoding device. In other examples, a source device and a destinationdevice may include other components or arrangements. For example, sourcedevice 102 may receive video data from an external video source, such asan external camera. Likewise, destination device 116 may interface withan external display device, rather than including an integrated displaydevice.

System 100 as shown in FIG. 1 is merely one example. In general, anydigital video encoding and/or decoding device may perform techniques forcoding MTS data. Source device 102 and destination device 116 are merelyexamples of such coding devices in which source device 102 generatescoded video data for transmission to destination device 116. Thisdisclosure refers to a “coding” device as a device that performs coding(encoding and/or decoding) of data. Thus, video encoder 200 and videodecoder 300 represent examples of coding devices, in particular, a videoencoder and a video decoder, respectively. In some examples, devices102, 116 may operate in a substantially symmetrical manner such thateach of devices 102, 116 include video encoding and decoding components.Hence, system 100 may support one-way or two-way video transmissionbetween video devices 102, 116, e.g., for video streaming, videoplayback, video broadcasting, or video telephony.

In general, video source 104 represents a source of video data (i.e.,raw, uncoded video data) and provides a sequential series of pictures(also referred to as “frames”) of the video data to video encoder 200,which encodes data for the pictures. Video source 104 of source device102 may include a video capture device, such as a video camera, a videoarchive containing previously captured raw video, and/or a video feedinterface to receive video from a video content provider. As a furtheralternative, video source 104 may generate computer graphics-based dataas the source video, or a combination of live video, archived video, andcomputer-generated video. In each case, video encoder 200 encodes thecaptured, pre-captured, or computer-generated video data. Video encoder200 may rearrange the pictures from the received order (sometimesreferred to as “display order”) into a coding order for coding. Videoencoder 200 may generate a bitstream including encoded video data.Source device 102 may then output the encoded video data via outputinterface 108 onto computer-readable medium 110 for reception and/orretrieval by, e.g., input interface 122 of destination device 116.

Memory 106 of source device 102 and memory 120 of destination device 116represent general purpose memories. In some example, memories 106, 120may store raw video data, e.g., raw video from video source 104 and raw,decoded video data from video decoder 300. Additionally oralternatively, memories 106, 120 may store software instructionsexecutable by, e.g., video encoder 200 and video decoder 300,respectively. Although shown separately from video encoder 200 and videodecoder 300 in this example, it should be understood that video encoder200 and video decoder 300 may also include internal memories forfunctionally similar or equivalent purposes. Furthermore, memories 106,120 may store encoded video data, e.g., output from video encoder 200and input to video decoder 300. In some examples, portions of memories106, 120 may be allocated as one or more video buffers, e.g., to storeraw, decoded, and/or encoded video data.

Computer-readable medium 110 may represent any type of medium or devicecapable of transporting the encoded video data from source device 102 todestination device 116. In one example, computer-readable medium 110represents a communication medium to enable source device 102 totransmit encoded video data directly to destination device 116 inreal-time, e.g., via a radio frequency network or computer-basednetwork. Output interface 108 may modulate a transmission signalincluding the encoded video data, and input interface 122 may demodulatethe received transmission signal, according to a communication standard,such as a wireless communication protocol. The communication medium maycomprise any wireless or wired communication medium, such as a radiofrequency (RF) spectrum or one or more physical transmission lines. Thecommunication medium may form part of a packet-based network, such as alocal area network, a wide-area network, or a global network such as theInternet. The communication medium may include routers, switches, basestations, or any other equipment that may be useful to facilitatecommunication from source device 102 to destination device 116.

In some examples, source device 102 may output encoded data from outputinterface 108 to storage device 112. Similarly, destination device 116may access encoded data from storage device 112 via input interface 122.Storage device 116 may include any of a variety of distributed orlocally accessed data storage media such as a hard drive, Blu-ray discs,DVDs, CD-ROMs, flash memory, volatile or non-volatile memory, or anyother suitable digital storage media for storing encoded video data.

In some examples, source device 102 may output encoded video data tofile server 114 or another intermediate storage device that may storethe encoded video generated by source device 102. Destination device 116may access stored video data from file server 114 via streaming ordownload. File server 114 may be any type of server device capable ofstoring encoded video data and transmitting that encoded video data tothe destination device 116. File server 114 may represent a web server(e.g., for a website), a File Transfer Protocol (FTP) server, a contentdelivery network device, or a network attached storage (NAS) device.Destination device 116 may access encoded video data from file server114 through any standard data connection, including an Internetconnection. This may include a wireless channel (e.g., a Wi-Ficonnection), a wired connection (e.g., DSL, cable modem, etc.), or acombination of both that is suitable for accessing encoded video datastored on file server 114. File server 114 and input interface 122 maybe configured to operate according to a streaming transmission protocol,a download transmission protocol, or a combination thereof.

Output interface 108 and input interface 122 may represent wirelesstransmitters/receiver, modems, wired networking components (e.g.,Ethernet cards), wireless communication components that operateaccording to any of a variety of IEEE 802.11 standards, or otherphysical components. In examples where output interface 108 and inputinterface 122 comprise wireless components, output interface 108 andinput interface 122 may be configured to transfer data, such as encodedvideo data, according to a cellular communication standard, such as 4G,4G-LTE (Long-Term Evolution), LTE Advanced, 5G, or the like. In someexamples where output interface 108 comprises a wireless transmitter,output interface 108 and input interface 122 may be configured totransfer data, such as encoded video data, according to other wirelessstandards, such as an IEEE 802.11 specification, an IEEE 802.15specification (e.g., ZigBee™), a Bluetooth™ standard, or the like. Insome examples, source device 102 and/or destination device 116 mayinclude respective system-on-a-chip (SoC) devices. For example, sourcedevice 102 may include an SoC device to perform the functionalityattributed to video encoder 200 and/or output interface 108, anddestination device 116 may include an SoC device to perform thefunctionality attributed to video decoder 300 and/or input interface122.

The techniques of this disclosure may be applied to video coding insupport of any of a variety of multimedia applications, such asover-the-air television broadcasts, cable television transmissions,satellite television transmissions, Internet streaming videotransmissions, such as dynamic adaptive streaming over HTTP (DASH),digital video that is encoded onto a data storage medium, decoding ofdigital video stored on a data storage medium, or other applications.

Input interface 122 of destination device 116 receives an encoded videobitstream from computer-readable medium 110 (e.g., storage device 112,file server 114, or the like). The encoded video bitstream ofcomputer-readable medium 110 may include signaling information definedby video encoder 200, which is also used by video decoder 300, such assyntax elements having values that describe characteristics and/orprocessing of video blocks or other coded units (e.g., slices, pictures,groups of pictures, sequences, or the like). Display device 118 displaysdecoded pictures of the decoded video data to a user. Display device 118may represent any of a variety of display devices such as a cathode raytube (CRT), a liquid crystal display (LCD), a plasma display, an organiclight emitting diode (OLED) display, or another type of display device.

Although not shown in FIG. 1 , in some examples, video encoder 200 andvideo decoder 300 may each be integrated with an audio encoder and/oraudio decoder, and may include appropriate MUX-DEMUX units, or otherhardware and/or software, to handle multiplexed streams including bothaudio and video in a common data stream. If applicable, MUX-DEMUX unitsmay conform to the ITU H.223 multiplexer protocol, or other protocolssuch as the user datagram protocol (UDP).

Video encoder 200 and video decoder 300 each may be implemented as anyof a variety of suitable encoder and/or decoder circuitry, such as oneor more microprocessors, digital signal processors (DSPs), applicationspecific integrated circuits (ASICs), field programmable gate arrays(FPGAs), discrete logic, software, hardware, firmware or anycombinations thereof. When the techniques are implemented partially insoftware, a device may store instructions for the software in asuitable, non-transitory computer-readable medium and execute theinstructions in hardware using one or more processors to perform thetechniques of this disclosure. Each of video encoder 200 and videodecoder 300 may be included in one or more encoders or decoders, eitherof which may be integrated as part of a combined encoder/decoder (CODEC)in a respective device. A device including video encoder 200 and/orvideo decoder 300 may comprise an integrated circuit, a microprocessor,and/or a wireless communication device, such as a cellular telephone.

Video encoder 200 and video decoder 300 may operate according to a videocoding standard, such as ITU-T H.265, also referred to as HighEfficiency Video Coding (HEVC) or extensions thereto, such as themulti-view and/or scalable video coding extensions. Alternatively, videoencoder 200 and video decoder 300 may operate according to otherproprietary or industry standards, such as the upcoming Versatile VideoCoding (VVC) standard, which is planned to become ITU-T H.266. A workingdraft of VVC is Bross et al., “Versatile Video Coding (Draft 5)” JointVideo Experts Team (JVET) of ITU-T SG 16 WP 3 and ISO/IEC JTC 1/SC 29/WG11, 14th Meeting, Geneva, CH, 19-27 Mar. 2019, document JVET-N1001-v5.The techniques of this disclosure, however, are not limited to anyparticular coding standard.

In general, video encoder 200 and video decoder 300 may performblock-based coding of pictures. The term “block” generally refers to astructure including data to be processed (e.g., encoded, decoded, orotherwise used in the encoding and/or decoding process). For example, ablock may include a two-dimensional matrix of samples of luminanceand/or chrominance data. In general, video encoder 200 and video decoder300 may code video data represented in a YUV (e.g., Y, Cb, Cr) format.That is, rather than coding red, green, and blue (RGB) data for samplesof a picture, video encoder 200 and video decoder 300 may code luminanceand chrominance components, where the chrominance components may includeboth red hue and blue hue chrominance components. In some examples,video encoder 200 converts received RGB formatted data to a YUVrepresentation prior to encoding, and video decoder 300 converts the YUVrepresentation to the RGB format. Alternatively, pre- andpost-processing units (not shown) may perform these conversions.

This disclosure may generally refer to coding (e.g., encoding anddecoding) of pictures to include the process of encoding or decodingdata of the picture. Similarly, this disclosure may refer to coding ofblocks of a picture to include the process of encoding or decoding datafor the blocks, e.g., prediction and/or residual coding. An encodedvideo bitstream generally includes a series of values for syntaxelements representative of coding decisions (e.g., coding modes) andpartitioning of pictures into blocks. Thus, references to coding apicture or a block should generally be understood as coding values forsyntax elements forming the picture or block.

HEVC defines various blocks, including coding units (CUs), predictionunits (PUs), and transform units (TUs). According to HEVC, a video coder(such as video encoder 200) partitions a coding tree unit (CTU) into CUsaccording to a quadtree structure. That is, the video coder partitionsCTUs and CUs into four equal, non-overlapping squares, and each node ofthe quadtree has either zero or four child nodes. Nodes without childnodes may be referred to as “leaf nodes,” and CUs of such leaf nodes mayinclude one or more PUs and/or one or more TUs. The video coder mayfurther partition PUs and TUs. For example, in HEVC, a residual quadtree(RQT) represents partitioning of TUs. In HEVC, PUs representinter-prediction data, while TUs represent residual data. CUs that areintra-predicted include intra-prediction information, such as anintra-mode indication.

As another example, video encoder 200 and video decoder 300 may beconfigured to operate according to VVC. According to VVC, a video coder(such as video encoder 200) partitions a picture into a plurality ofcoding tree units (CTUs). Video encoder 200 may partition a CTUaccording to a tree structure, such as a quadtree-binary tree (QTBT)structure. The QTBT structure of VVC removes the concepts of multiplepartition types, such as the separation between CUs, PUs, and TUs ofHEVC. A QTBT structure of VVC includes two levels: a first levelpartitioned according to quadtree partitioning, and a second levelpartitioned according to binary tree partitioning. A root node of theQTBT structure corresponds to a CTU. Leaf nodes of the binary treescorrespond to coding units (CUs).

In some examples, video encoder 200 and video decoder 300 may use asingle QTBT structure to represent each of the luminance and chrominancecomponents, while in other examples, video encoder 200 and video decoder300 may use two or more QTBT structures, such as one QTBT structure forthe luminance component and another QTBT structure for both chrominancecomponents (or two QTBT structures for respective chrominancecomponents).

Video encoder 200 and video decoder 300 may be configured to usequadtree partitioning per HEVC, QTBT partitioning according to VVC, orother partitioning structures. For purposes of explanation, thedescription of the techniques of this disclosure is presented withrespect to QTBT partitioning. However, it should be understood that thetechniques of this disclosure may also be applied to video codersconfigured to use quadtree partitioning, or other types of partitioningas well.

This disclosure may use “N×N” and “N by N” interchangeably to refer tothe sample dimensions of a block (such as a CU or other video block) interms of vertical and horizontal dimensions, e.g., 16×16 samples or 16by 16 samples. In general, a 16×16 CU will have 16 samples in a verticaldirection (y=16) and 16 samples in a horizontal direction (x=16).Likewise, an N×N CU generally has N samples in a vertical direction andN samples in a horizontal direction, where N represents a nonnegativeinteger value. The samples in a CU may be arranged in rows and columns.Moreover, CUs need not necessarily have the same number of samples inthe horizontal direction as in the vertical direction. For example, CUsmay comprise N×M samples, where M is not necessarily equal to N.

Video encoder 200 encodes video data for CUs representing predictionand/or residual information, and other information. The predictioninformation indicates how the CU is to be predicted in order to form aprediction block for the CU. The residual information generallyrepresents sample-by-sample differences between samples of the CU priorto encoding and the prediction block.

To predict a CU, video encoder 200 may generally form a prediction blockfor the CU through inter-prediction or intra-prediction.Inter-prediction generally refers to predicting the CU from data of apreviously coded picture, whereas intra-prediction generally refers topredicting the CU from previously coded data of the same picture. Toperform inter-prediction, video encoder 200 may generate the predictionblock using one or more motion vectors. Video encoder 200 may generallyperform a motion search to identify a reference block that closelymatches the CU, e.g., in terms of differences between the CU and thereference block. Video encoder 200 may calculate a difference metricusing a sum of absolute difference (SAD), sum of squared differences(SSD), mean absolute difference (MAD), mean squared differences (MSD),or other such difference calculations to determine whether a referenceblock closely matches the current CU. In some examples, video encoder200 may predict the current CU using uni-directional prediction orbi-directional prediction.

VVC also provides an affine motion compensation mode, which may beconsidered an inter-prediction mode. In affine motion compensation mode,video encoder 200 may determine two or more motion vectors thatrepresent non-translational motion, such as zoom in or out, rotation,perspective motion, or other irregular motion types.

To perform intra-prediction, video encoder 200 may select anintra-prediction mode to generate the prediction block. VVC providessixty-seven intra-prediction modes, including various directional modes,as well as planar mode and DC mode. In general, video encoder 200selects an intra-prediction mode that describes neighboring samples to acurrent block (e.g., a block of a CU) from which to predict samples ofthe current block. Such samples may generally be above, above and to theleft, or to the left of the current block in the same picture as thecurrent block, assuming video encoder 200 codes CTUs and CUs in rasterscan order (left to right, top to bottom).

Video encoder 200 encodes data representing the prediction mode for acurrent block. For example, for inter-prediction modes, video encoder200 may encode data representing which of the various availableinter-prediction modes is used, as well as motion information for thecorresponding mode. For uni-directional or bi-directionalinter-prediction, for example, video encoder 200 may encode motionvectors using advanced motion vector prediction (AMVP) or merge mode.Video encoder 200 may use similar modes to encode motion vectors foraffine motion compensation mode.

Following prediction, such as intra-prediction or inter-prediction of ablock, video encoder 200 may calculate residual data for the block. Theresidual data, such as a residual block, represents sample by sampledifferences between the block and a prediction block for the block,formed using the corresponding prediction mode. Video encoder 200 mayapply one or more transforms to the residual block, to producetransformed data in a transform domain instead of the sample domain. Forexample, video encoder 200 may apply a discrete cosine transform (DCT),an integer transform, a wavelet transform, or a conceptually similartransform to residual video data. Additionally, video encoder 200 mayapply a secondary transform following the first transform, such as amode-dependent non-separable secondary transform (MDNSST), a signaldependent transform, a Karhunen-Loeve transform (KLT), or the like.Video encoder 200 produces transform coefficients following applicationof the one or more transforms.

In accordance with the techniques of this disclosure, video encoder 200may determine a particular type of transform (or multiple transform) toapply to a residual block for a current block. The determined type oftransform may include a primary transform, which may be a separabletransform including a horizontal transform and a vertical transform. Insome examples, the determined type of transform may further include asecondary transform (e.g., a nonseparable transform). Video encoder 200may encode a first codeword representing the selected type of transform,which represents the primary transform and whether or not the selectedtype of transform includes a secondary transform. In the case that thefirst codeword indicates that the selected type of transform includesthe secondary transform, video encoder 200 may further encode a secondcodeword representing a selected secondary transform of a set ofavailable secondary transforms. Furthermore, video encoder 200 may applyboth the primary transform and the secondary transform. Examples of suchcombinations of codewords are explained in greater detail below withrespect to Tables 1-12 and FIGS. 6-8 .

As noted above, following any transforms to produce transformcoefficients, video encoder 200 may perform quantization of thetransform coefficients. Quantization generally refers to a process inwhich transform coefficients are quantized to possibly reduce the amountof data used to represent the coefficients, providing furthercompression. By performing the quantization process, video encoder 200may reduce the bit depth associated with some or all of thecoefficients. For example, video encoder 200 may round an n-bit valuedown to an m-bit value during quantization, where n is greater than m.In some examples, to perform quantization, video encoder 200 may performa bitwise right-shift of the value to be quantized.

Following quantization, video encoder 200 may scan the transformcoefficients, producing a one-dimensional vector from thetwo-dimensional matrix including the quantized transform coefficients.The scan may be designed to place higher energy (and therefore lowerfrequency) coefficients at the front of the vector and to place lowerenergy (and therefore higher frequency) transform coefficients at theback of the vector. In some examples, video encoder 200 may utilize apredefined scan order to scan the quantized transform coefficients toproduce a serialized vector, and then entropy encode the quantizedtransform coefficients of the vector. In other examples, video encoder200 may perform an adaptive scan. After scanning the quantized transformcoefficients to form the one-dimensional vector, video encoder 200 mayentropy encode the one-dimensional vector, e.g., according tocontext-adaptive binary arithmetic coding (CABAC). Video encoder 200 mayalso entropy encode values for syntax elements describing metadataassociated with the encoded video data for use by video decoder 300 indecoding the video data.

To perform CABAC, video encoder 200 may assign a context within acontext model to a symbol to be transmitted. The context may relate to,for example, whether neighboring values of the symbol are zero-valued ornot. The probability determination may be based on a context assigned tothe symbol.

Video encoder 200 may further generate syntax data, such as block-basedsyntax data, picture-based syntax data, and sequence-based syntax data,to video decoder 300, e.g., in a picture header, a block header, a sliceheader, or other syntax data, such as a sequence parameter set (SPS),picture parameter set (PPS), or video parameter set (VPS). Video decoder300 may likewise decode such syntax data to determine how to decodecorresponding video data.

In this manner, video encoder 200 may generate a bitstream includingencoded video data, e.g., syntax elements describing partitioning of apicture into blocks (e.g., CUs) and prediction and/or residualinformation for the blocks. Ultimately, video decoder 300 may receivethe bitstream and decode the encoded video data.

In general, video decoder 300 performs a reciprocal process to thatperformed by video encoder 200 to decode the encoded video data of thebitstream. For example, video decoder 300 may decode values for syntaxelements of the bitstream using CABAC in a manner substantially similarto, albeit reciprocal to, the CABAC encoding process of video encoder200. The syntax elements may define partitioning information of apicture into CTUs, and partitioning of each CTU according to acorresponding partition structure, such as a QTBT structure, to defineCUs of the CTU. The syntax elements may further define prediction andresidual information for blocks (e.g., CUs) of video data.

The residual information may be represented by, for example, quantizedtransform coefficients. Video decoder 300 may inverse quantize andinverse transform the quantized transform coefficients of a block toreproduce a residual block for the block.

In accordance with the techniques of this disclosure, video decoder 300may decode a first codeword representing a type of transform to beapplied to decoded transform coefficients for a current block of videodata. As discussed above, the type of transform may represent a primarytransform, which may be a separable transform including a horizontaltransform and a vertical transform. The type of transform may furtherinclude a secondary transform. If the type of transform includes thesecondary transform, video decoder 300 may decode a second codewordrepresenting the secondary transform, which may be included in a set ofavailable secondary transforms. Video decoder 300 may then apply thesecondary transform to the decoded transform coefficients to produce anintermediate set of transform coefficients, then apply the primarytransform to the intermediate set of transform coefficients to reproducea residual block for the current block.

Video decoder 300 uses a signaled prediction mode (intra- orinter-prediction) and related prediction information (e.g., motioninformation for inter-prediction) to form a prediction block for theblock. Video decoder 300 may then combine the prediction block and theresidual block (on a sample-by-sample basis) to reproduce the originalblock. Video decoder 300 may perform additional processing, such asperforming a deblocking process to reduce visual artifacts alongboundaries of the block.

As mentioned above, video encoder 200 and video decoder 300 may applyCABAC encoding and decoding to values of syntax elements. To apply CABACencoding to a syntax element, video encoder 200 may binarize the valueof the syntax element to form a series of one or more bits, which arereferred to as “bins.” In addition, video encoder 200 may identify acoding context. The coding context may identify probabilities of binshaving particular values. For instance, a coding context may indicate a0.7 probability of coding a 0-valued bin and a 0.3 probability of codinga 1-valued bin. After identifying the coding context, video encoder 200may divide an interval into a lower sub-interval and an uppersub-interval. One of the sub-intervals may be associated with the value0 and the other sub-interval may be associated with the value 1.

The widths of the sub-intervals may be proportional to the probabilitiesindicated for the associated values by the identified coding context. Ifa bin of the syntax element has the value associated with the lowersub-interval, the encoded value may be equal to the lower boundary ofthe lower sub-interval. If the same bin of the syntax element has thevalue associated with the upper sub-interval, the encoded value may beequal to the lower boundary of the upper sub-interval. To encode thenext bin of the syntax element, video encoder 200 may repeat these stepswith the interval being the sub-interval associated with the value ofthe encoded bit. When video encoder 200 repeats these steps for the nextbin, video encoder 200 may use modified probabilities based on theprobabilities indicated by the identified coding context and the actualvalues of bins encoded.

When video decoder 300 performs CABAC decoding on a value of a syntaxelement, video decoder 300 may identify a coding context. Video decoder300 may then divide an interval into a lower sub-interval and an uppersub-interval. One of the sub-intervals may be associated with the value0 and the other sub-interval may be associated with the value 1. Thewidths of the sub-intervals may be proportional to the probabilitiesindicated for the associated values by the identified coding context. Ifthe encoded value is within the lower sub-interval, video decoder 300may decode a bin having the value associated with the lowersub-interval. If the encoded value is within the upper sub-interval,video decoder 300 may decode a bin having the value associated with theupper sub-interval. To decode a next bin of the syntax element, videodecoder 300 may repeat these steps with the interval being thesub-interval that contains the encoded value. When video decoder 300repeats these steps for the next bin, video decoder 300 may use modifiedprobabilities based on the probabilities indicated by the identifiedcoding context and the decoded bins. Video decoder 300 may then inversebinarize the bins to recover the value of the syntax element.

In video coding standards prior to HEVC, only a fixed separabletransform is used where DCT-2 is used both vertically and horizontally.In HEVC, in addition to DCT-2, DST-7 is also employed for 4×4 blocks asa fixed separable transform.

U.S. Pat. No. 10,306,229, U.S. Patent Publication 2018/0020218, and U.S.Provisional Patent application 62/679,570 describe multiple transformselection (MTS) techniques. MTS was previously called Adaptive MultipleTransforms (AMT). An example of MTS in U.S. Provisional Patentapplication 62/679,570 has been adopted in the Joint Experimental Model(JEM-7.0) of the Joint Video Experts Team (JVET), and later a simplifiedversion of MTS is adopted in VVC.

This disclosure may generally refer to “signaling” certain information,such as syntax elements. The term “signaling” may generally refer to thecommunication of values syntax elements and/or other data used to decodeencoded video data. That is, video encoder 200 may signal values forsyntax elements in the bitstream. In general, signaling refers togenerating a value in the bitstream. As noted above, source device 102may transport the bitstream to destination device 116 substantially inreal time, or not in real time, such as might occur when storing syntaxelements to storage device 112 for later retrieval by destination device116.

FIGS. 2A and 2B are conceptual diagram illustrating an example quadtreebinary tree (QTBT) structure 130, and a corresponding coding tree unit(CTU) 132. The solid lines represent quadtree splitting, and dottedlines indicate binary tree splitting. In each split (i.e., non-leaf)node of the binary tree, one flag is signaled to indicate whichsplitting type (i.e., horizontal or vertical) is used, where 0 indicateshorizontal splitting and 1 indicates vertical splitting in this example.For the quadtree splitting, there is no need to indicate the splittingtype, since quadtree nodes split a block horizontally and verticallyinto 4 sub-blocks with equal size. Accordingly, video encoder 200 mayencode, and video decoder 300 may decode, syntax elements (such assplitting information) for a region tree level of QTBT structure 130(i.e., the solid lines) and syntax elements (such as splittinginformation) for a prediction tree level of QTBT structure 130 (i.e.,the dashed lines). Video encoder 200 may encode, and video decoder 300may decode, video data, such as prediction and transform data, for CUsrepresented by terminal leaf nodes of QTBT structure 130.

In general, CTU 132 of FIG. 2B may be associated with parametersdefining sizes of blocks corresponding to nodes of QTBT structure 130 atthe first and second levels. These parameters may include a CTU size(representing a size of CTU 132 in samples), a minimum quadtree size(MinQTSize, representing a minimum allowed quadtree leaf node size), amaximum binary tree size (MaxBTSize, representing a maximum allowedbinary tree root node size), a maximum binary tree depth (MaxBTDepth,representing a maximum allowed binary tree depth), and a minimum binarytree size (MinBTSize, representing the minimum allowed binary tree leafnode size).

The root node of a QTBT structure corresponding to a CTU may have fourchild nodes at the first level of the QTBT structure, each of which maybe partitioned according to quadtree partitioning. That is, nodes of thefirst level are either leaf nodes (having no child nodes) or have fourchild nodes. The example of QTBT structure 130 represents such nodes asincluding the parent node and child nodes having solid lines forbranches. Nodes of the first level that are not larger than the maximumallowed binary tree root node size (MaxBTSize) can be furtherpartitioned by respective binary trees. The binary tree splitting of onenode can be iterated until the nodes resulting from the split reach theminimum allowed binary tree leaf node size (MinBTSize) or the maximumallowed binary tree depth (MaxBTDepth). The example of QTBT structure130 represents such nodes as having dashed lines for branches. Thebinary tree leaf node is referred to as a coding unit (CU), which isused for prediction (e.g., intra-picture or inter-picture prediction)and transform, without any further partitioning. As discussed above, CUsmay also be referred to as “video blocks” or “blocks.”

In one example of the QTBT partitioning structure, the CTU size is setas 128×128 (luma samples and two corresponding 64×64 chroma samples),the MinQTSize is set as 16×16, the MaxBTSize is set as 64×64, theMinBTSize (for both width and height) is set as 4, and the MaxBTDepth isset as 4. The quadtree partitioning is applied to the CTU first togenerate quad-tree leaf nodes. The quadtree leaf nodes may have a sizefrom 16×16 (i.e., the MinQTSize) to 128×128 (i.e., the CTU size). If theleaf quadtree node is 128×128, it will not be further split by thebinary tree, since the size exceeds the MaxBTSize (i.e., 64×64, in thisexample). Otherwise, the leaf quadtree node will be further partitionedby the binary tree. Therefore, the quadtree leaf node is also the rootnode for the binary tree and has the binary tree depth as 0. When thebinary tree depth reaches MaxBTDepth (4, in this example), no furthersplitting is permitted. When the binary tree node has width equal toMinBTSize (4, in this example), it implies no further horizontalsplitting is permitted. Similarly, a binary tree node having a heightequal to MinBTSize implies no further vertical splitting is permittedfor that binary tree node. As noted above, leaf nodes of the binary treeare referred to as CUs, and are further processed according toprediction and transform without further partitioning.

FIGS. 3A and 3B are conceptual diagrams illustrating an exampletransform scheme based on a residual quadtree of HEVC. In HEVC, atransform coding structure using the residual quadtree (RQT) is appliedto adapt various characteristics of residual blocks, which is brieflydescribed as follows, adapted fromwww.hhi.fraunhofer.de/fields-of-competence/image-processing/research-groups/image-video-coding/hevc-high-efficiency-video-coding/transform-coding-using-the-residual-quadtree-rqt.html.

In HEVC, each picture is divided into coding tree units (CTU), which arecoded in raster scan order for a specific tile or slice. A CTU is asquare block and represents the root of a quadtree, i.e., the codingtree. The CTU size may range from 8×8 to 64×64 luma samples, buttypically 64×64 is used. Each CTU can be further split into smallersquare blocks called coding units (CUs).

After the CTU is split recursively into CUs, each CU is further dividedinto prediction units (PU) and transform units (TU). The partitioning ofa CU into TUs is carried out recursively based on a quadtree approach,therefore the residual signal of each CU is coded by a tree structurenamely, the residual quadtree (RQT). The RQT allows TU sizes from 4×4 upto 32×32 luma samples.

FIG. 3A depicts an example where a CU includes 10 TUs, labeled with theletters a to j, and the corresponding block partitioning. Each node ofthe RQT shown in FIG. 3B is actually a transform unit (TU) correspondingto FIG. 3A. The individual TUs are processed in depth-first treetraversal order, which is illustrated in FIG. 3A as alphabetical order,which follows a recursive Z-scan with depth-first traversal. Thequadtree approach enables the adaptation of the transform to the varyingspace-frequency characteristics of the residual signal.

Typically, larger transform block sizes, which have larger spatialsupport, provide better frequency resolution. However, smaller transformblock sizes, which have smaller spatial support, provide better spatialresolution. The trade-off between the two, spatial and frequencyresolutions, is chosen by the encoder mode decision, for example basedon rate-distortion optimization technique. The rate-distortionoptimization technique calculates a weighted sum of coding bits andreconstruction distortion, i.e., the rate-distortion cost, for eachcoding mode (e.g., a specific RQT splitting structure), and select thecoding mode with least rate-distortion cost as the best mode.

Three parameters are defined in the RQT per HEVC: the maximum depth ofthe tree, the minimum allowed transform size and the maximum allowedtransform size. The minimum and maximum transform sizes can vary withinthe range from 4×4 to 32×32 samples, which correspond to the supportedblock transforms mentioned in the previous paragraph. The maximumallowed depth of the RQT restricts the number of TUs. A maximum depthequal to zero means that a CB cannot be split any further if eachincluded TB reaches the maximum allowed transform size, e.g., 32×32.

All these parameters interact and influence the RQT structure in HEVC.Consider a case in which the root CB size is 64×64, the maximum depth isequal to zero, and the maximum transform size is equal to 32×32. In thiscase, the CB has to be partitioned at least once, since otherwise itwould lead to a 64×64 TB, which is not allowed. The RQT parameters,i.e., maximum RQT depth, minimum and maximum transform size, aretransmitted in the bitstream at the sequence parameter set level, perHEVC. Regarding the RQT depth, different values can be specified andsignaled for intra and inter coded CUs.

The quadtree transform is applied for both Intra and Inter residualblocks in HEVC. Typically, the DCT-II transform of the same size of thecurrent residual quadtree partition is applied for a residual block.However, if the current residual quadtree block is 4×4 and is generatedby Intra prediction, the above 4×4 DST-VII transform is applied.

In HEVC, larger size transforms, e.g., 64×64 transform, are not adopted,mainly due to their limited benefit considering the relatively highcomplexity for relatively smaller resolution videos.

FIG. 4 is a block diagram illustrating an example system 140 for hybridvideo encoding with adaptive transform selection. The techniques of thisdisclosure may be performed by such a system, or a correspondingdecoding system. In general, the techniques of this disclosure areapplicable to an adaptive transform coding scheme, where for each blockof prediction residuals, different transforms can be selected by a videoencoder, signaled as side information, and determined by a video decoderusing the side information.

System 140 of FIG. 4 includes block separation unit 142, blockprediction unit 144, residual generation unit 146, block transformationunit 148, transform bank 150, quantization unit 152, entropy encodingunit 154, inverse quantization unit 156, inverse block transformationunit 158, block reconstruction unit 160, and frame buffer 162. Blockseparation unit 142 generally receives raw, uncoded video data andpartitions pictures of the video data into blocks. Block prediction unit144 generates a prediction block for a current block of video data to beencoded. Block separation unit 142 provides the current block toresidual generation unit 146 and block prediction unit 144 provides theprediction block to residual generation unit 146. Residual generationunit 146 generates a residual block (r) and provides the residual blockto block transformation unit 148.

Block transformation unit 148 selects one or more transforms fromtransform bank 150. For example, according to the techniques of thisdisclosure, transform bank 150 may include one or more primarytransforms (e.g., separable transforms) and one or more secondarytransforms (e.g., non-separable transforms). Block transformation unit148 may then apply the primary and, if applicable, the secondarytransform to generate transform coefficients. Furthermore, blocktransformation unit 148 may send an indication (t) of the transform(s)to entropy encoding unit 154. Block transformation unit 148 provides thetransform coefficients (T^((t))r) to quantization unit 152.

Quantization unit 152 quantizes the transform coefficients, e.g., byreducing bit depth of the transform coefficients according to aquantization parameter (QP) for the current block. Quantization unit 152provides the quantized transform coefficients to entropy encoding unit154 and inverse quantization unit 156.

Entropy encoding unit 154 performs entropy encoding of values for syntaxelements, including the indications of transforms (t) and quantizedtransform coefficients. In accordance with the techniques of thisdisclosure, entropy encoding unit 154 may encode a first codewordrepresenting a selected transform scheme of a set of transformcandidates of a multiple transform selection (MTS) scheme for a currentblock of video data. The selected transform scheme may include a primarytransform and, in some examples, a secondary transform to be applied inaddition to the primary transform. In the case the selected transformscheme includes the secondary transform, entropy encoding unit 154 mayencode a second codeword representing the secondary transform in a setof available secondary transforms. Entropy encoding unit 154 may includethe entropy encoded data (e.g., the first and/or second codewords andentropy encoded syntax elements for the quantized transformcoefficients) in an encoded video bitstream.

Inverse quantization unit 156 may inverse quantize the quantizedtransform coefficients and pass the resulting transform coefficients toinverse block transformation unit 158. Inverse block transformation unit158 may apply the primary transform and, if applicable, the secondarytransform to the transform coefficients to reproduce the residual block.Inverse block transformation unit 158 may provide the residual block toblock reconstruction unit 160, which may combine the residual block withthe prediction block to produce a reconstructed block, and store thereconstructed block in frame buffer 162. Frame buffer 162 may also bereferred to as a decoded picture buffer (DPB).

Each of the various components of FIG. 4 may be implemented in hardware,software, firmware, or a combination thereof. When implemented insoftware or firmware, instructions for the various operations may bestored in a memory and executed by one or more processing units. Theprocessing units and memory may be implemented in circuitry. Theprocessing units may include, for example, one or more digital signalprocessors (DSPs), general purpose microprocessors, application specificintegrated circuits (ASICs), field programmable gate arrays (FPGAs), orother equivalent integrated or discrete logic circuitry, in anycombination.

In this manner, system 140 of FIG. 4 represents an example of a videoencoder including a memory configured to store video data; and one ormore processors implemented in circuitry and configured to: code a firstcodeword representing a selected transform scheme of a set of transformcandidates of a multiple transform selection (MTS) scheme for a currentblock of video data, the selected transform scheme being a secondarytransform of a set of available secondary transforms to be applied inaddition to a primary transform; code a second codeword representing thesecondary transform from the set of available secondary transforms; andapply the primary transform and the secondary transform during coding ofresidual data for the current block.

FIGS. 5A and 5B are conceptual diagrams illustrating horizontal andvertical transforms as a separate transform implementation. Inparticular, horizontal and vertical lines of residual values may betransformed independently using the horizontal and vertical transforms(e.g., to reduce computational complexity, the block transforms may becomputed in a separable manner).

In video coding standards prior to HEVC, only a fixed separabletransform is used where DCT-2 is used both vertically and horizontally.In HEVC, in addition to DCT-2, DST-7 is also employed for 4×4 blocks asa fixed separable transform. U.S. patent application Ser. Nos.15/005,736 and 15/649,612 describe adaptive extensions of those fixedtransforms, and an example of MTS (also referred to as adaptive multipletransforms (AMT)) is described in U.S. patent application Ser. No.15/005,736, filed Jan. 25, 2016; Ser. No. 15/649,612, filed Jul. 13,2017; and 62/679,570 filed Jun. 1, 2018 has been adopted in the JointExperimental Model (JEM) of the Joint Video Experts Team (JVET) (JointVideo Experts Team (JVET) of ITU-T SG 16 WP 3 and ISO/IEC JTC 1/SC 29/WG11, JEM Software, available atjvet.hhi.fraunhofer.de/svn/svn_HMJEMSoftware/tags/HM-16.6-JEM-7.0.).

FIG. 6 is a conceptual diagram representing an example of MTS signalingused to identify two transforms. In the current version of VTM(Versatile Video Coding (Draft 4), Joint Video Experts Team (JVET),ITU-T SG 16 WP 3 and ISO/IEC JTC 1/SC 29/WG 11, 13th Meeting: Marrakech,Mass., 9-18 Jan. 2019, Document JVET-M1001, available atphenix.it-sudparis.eu/jvet/doc_end_user/documents/13_Marrakech/wg11/JVET-M1001-v7.zip),multiple transform candidates are signaled based on a truncated unarybinarization, which can be illustrated by concatenating binary tree inFIGS. 6 and 7 . Then, the transform candidates are associated with thecodewords obtained by the concatenation.

FIG. 7 is a conceptual diagram illustrating an example transformassignment and corresponding unary codewords. MTS Signaling in thecurrent version of VVC includes assigning transforms to codewordsobtained by concatenating the binary tree in FIG. 6 , where “H: DCT-8,V: DST-7” means DCT-8 is applied horizontally and DST-7 is appliedvertically for separable transformation, and IDT denotes 1-D identitytransform (performing scaling).

The MTS (multiple-transform-selection) design of VVC uses six transformcandidates (as in FIG. 7 ), and it supports combinations with DST-7 andDCT-8 other than using a single type of transform in both horizontal andvertical directions (i.e., applying IDT, DCT-2 and DST-7 horizontallyand vertically). In practice, a better coding efficiency can be achievedby allowing a larger number of transform candidates. This disclosuredescribes various extensions of the current MTS design that may improvecoding efficiency.

An MTS scheme may be defined by assigning transforms to codewords of aspecified signaling method. Video encoder 200 and/or video decoder 300may be configured according to the techniques of this disclosure, asdiscussed above and in greater detail below. In particular, an MTSscheme according to this disclosure may be defined by assigningtransforms to codewords of a specified signaling method. So, an MTSscheme may be completely defined by specifying: (i) a single set ormultiple sets of transforms (i.e., transform candidates), and (ii) anassociated signaling method. Thus, video encoder 200 and video decoder300 may be configured to code an indication of an MTS scheme using anyof the techniques of this disclosure, alone or in any combination.

The indication of the MTS scheme may be a codeword. In some examples,the MTS scheme may include both a primary transform, such as a separabletransform (e.g., a horizontal transform and a vertical transform), and asecondary transform. In such examples, video encoder 200 and videodecoder 300 may code a second codeword representing the secondarytransform, where the second codeword may identify the secondarytransform in a set of available secondary transforms.

The MTS design in VVC uses a single set of transforms including 6separable transform candidates as shown in Table 1 below:

TABLE 1 Transform candidates allowed in VVC as shown in FIG. 7 andcorresponding codewords used to signal the candidates CandidateHorizontal (H) Vertical (V) Codeword 1 IDT IDT 0 2 DCT-2 DCT-2 10 3DST-7 DST-7 110 4 DCT-8 DST-7 1110 5 DST-7 DCT-8 11110 6 DCT-8 DCT-811111

The example six transform candidates above may be signaled using thecodewords generated by concatenating a binary tree (FIG. 6 ) as shown inFIG. 7 (right). For each codeword, a transform candidate may be assignedas illustrated in FIG. 7 (left).

Alternative MTS designs may be defined based on one or more combinationsof the following techniques. That is, video encoder 200 and videodecoder 300 may perform any of the techniques described below, alone orin any combination.

-   -   1. The MTS design can be extended by including new transform        candidates with or without replacing the some of the current set        of candidates in VVC, shown in Table 1.    -   2. Combinations of DCT-2 and DST-7 can be included as additional        transform candidates.        -   a. In one example, two more transform candidates can be            added on top of the current VVC, so that in total 8            separable transform candidates are allowed as shown in Table            2:

TABLE 2 Transform candidates and associated codewords CandidateHorizontal (H) Vertical (V) Codeword 1 IDT IDT 0 2 DCT-2 DCT-2 10 3DST-7 DST-7 110 4 DCT-8 DST-7 1110 5 DST-7 DCT-8 11110 6 DCT-8 DCT-8111110 7 DCT-2 DST-7 1111110 8 DST-7 DCT-2 1111111

-   -   -   b. In another example, two more transform candidates can be            added by removing the “H:DCT-8,V:DCT-8” combination, so that            in total 7 separable transform candidates are allowed, as            shown in Table 3:

TABLE 3 Example transform candidates including combinations of DCT2 andDST7 without H: DCT-8, V: DCT-8 combination Candidate Horizontal (H)Vertical (V) Codeword 1 IDT IDT 0 2 DCT-2 DCT-2 10 3 DST-7 DST-7 110 4DCT-8 DST-7 1110 5 DST-7 DCT-8 11110 6 DCT-2 DST-7 111110 7 DST-7 DCT-2111111

-   -   3. Combinations of IDT and DST-7 can be included as additional        transform candidates.        -   a. For example, the following seven transform candidates may            be used in MTS, as shown in Table 4.

TABLE 4 Example transform candidates including combinations of IDT andDST7 without H: DCT-8, V: DCT-8 combination Candidate Horizontal (H)Vertical (V) Codeword 1 IDT IDT 0 2 DCT-2 DCT-2 10 3 DST-7 DST-7 110 4DCT-8 DST-7 1110 5 DST-7 DCT-8 11110 6 IDT DST-7 111110 7 DST-7 IDT111111

-   -   -   b. In another example, the following 10 transform candidates            may be used in MTS by adding combinations of DCT-2 and DST-7            as well as combinations of IDT and DST-7.

TABLE 5 Example transform candidates including combinations of DCT-2 andDST-7 as well as IDT and DST-7 by keeping the H: DCT-8, V: DCT-8combination as the 6th candidate Candidate Horizontal (H) Vertical (V)Codeword 1 IDT IDT 0 2 DCT-2 DCT-2 10 3 DST-7 DST-7 110 4 DCT-8 DST-71110 5 DST-7 DCT-8 11110 6 DCT-8 DCT-8 111110 7 IDT DST-7 1111110 8DST-7 IDT 11111110 9 DCT-2 DST-7 111111110 10 DST-7 DCT-2 111111111

-   -   -   c. In another example, the following 9 transform skip (which            is equivalent to applying the identity candidates may be            used in MTS by replacing DCT-8 and DCT-8 combination from            the above list as follows:

TABLE 6 Example transform candidates including combinations of DCT-2 andDST-7 as well as IDT and DST-7 by removing the H: DCT-8, V: DCT-8combination Candidate Horizontal (H) Vertical (V) Codeword 1 IDT IDT 0 2DCT-2 DCT-2 10 3 DST-7 DST-7 110 4 DCT-8 DST-7 1110 5 DST-7 DCT-8 111106 IDT DST-7 111110 7 DST-7 IDT 1111110 8 DCT-2 DST-7 11111110 9 DST-7DCT-2 11111111

-   -   4. The candidates and their associated binarization (i.e.,        codewords) may have a different ordering.        -   a. The ordering may be pre-defined and can be a fixed design            based on the statistics/frequency of each transform            candidate.        -   b. For example, the ordering can be done by ranking the            frequency of each transform candidate is used.        -   c. For example, it can be designed to reduce average            codeword length used to signal transform candidates (e.g.,            Huffman code generated based on the probability of each            candidate used).        -   d. For example, in a practical codec, H:DST-7, V:DST-7 and            H:DCT-2, V:DCT-2 combinations are frequently used.            Therefore, to reduce signaling overhead, the MTS design in            Table 1 can be ordered as in the following example of Table            7:

TABLE 7 Example of reordering the transform candidates in Table 1, where1st and 3rd transform candidates are swapped. Candidate Horizontal (H)Vertical (V) Codeword 1 DST-7 DST-7 0 2 DCT-2 DCT-2 10 3 IDT IDT 110 4DCT-8 DST-7 1110 5 DST-7 DCT-8 11110 6 DCT-8 DCT-8 11111

-   -   5. Depending on the prediction mode and/or block size, different        MTS designs can be used for coding a block, where a block can be        a transform unit (TU) or a coding unit (CU).        -   a. Different MTS designs may include:            -   i. different set of transform candidates;            -   ii. different signaling and binarization (i.e.,                codewords used for each candidate);            -   iii. both i) and ii) above.        -   b. Multiple MTS designs may be used to determine transform            choices depending on intra and/or inter prediction modes:            -   i. Different types of prediction methods (e.g., intra                and inter prediction) may use different MTS designs. For                example, for coding inter-predicted for blocks the MTS                defined in Table 1 may be used, while for                intra-predicted block the MTS defined in Table 5 may be                used to determine the transform.            -   ii. Different subsets of intra-prediction modes may use                different MTS designs. Different subsets of modes can be                defined by mutually exclusive and collectively                exhaustive selection of planar, DC and subsets of                angular modes. For example, for planar (0), DC (1) and                diagonal modes (34) the MTS design in Table 8 with 3                candidates can be used. For angular modes from (2) to                (33), Table 9 may be used. For or the rest of the                angular modes from (35) to (66), Table 10 may be used.

TABLE 8 Example of MTS design with 3 candidates Candidate Horizontal (H)Vertical (V) Codeword 1 IDT IDT 0 2 DCT-2 DCT-2 10 3 DST-7 DST-7 11

TABLE 9 Example of MTS design with 5 candidates Candidate Horizontal (H)Vertical (V) Codeword 1 IDT IDT 0 2 DCT-2 DCT-2 10 3 DST-7 DST-7 110 4DCT-8 DST-7 1110 5 DST-7 DCT-8 1111

TABLE 10 An example of MTS design with 5 candidates, where 4th and 5thcandidates in Table 9 are swapped Candidate Horizontal (H) Vertical (V)Codeword 1 IDT IDT 0 2 DCT-2 DCT-2 10 3 DST-7 DST-7 110 4 DST-7 DCT-81110 5 DCT-8 DST-7 1111

-   -   c. Multiple MTS designs may be used to determine transform        choices depending on block-shape and block-size.        -   i. Different MTS designs can be used for blocks of different            size and/or shape.        -   ii. For example, for coding small blocks, an MTS design with            fewer candidates may be used, while for larger blocks            another MTS design with more transform candidates may be            used. Thus, transform signaling overhead for small blocks            may be reduced.        -   iii. Small blocks. may be defined based on its width and/or            height. For example, blocks having width or height that are            less than 8 may be considered as small blocks, while            remaining blocks can be considered as large blocks (e.g., if            the minimum of width and height of a block is smaller than            16, then the block may be classified as small.).        -   iv. Blocks can also be classified based on            square/rectangular shape, where the ratio between width and            height can be used to classify blocks with different shapes            (e.g., 4×8 and 8×4 blocks may belong to one class, and            blocks of size 4×16 and 16×4 may belong to another class).        -   d. A single (unified) MTS design may also be used for            signaling.    -   6. Context derivation for signaling transform candidates can        also be made depending on one or combinations of the following:        -   a. block size;        -   b. block shape;        -   c. intra-mode;        -   d. inter-mode.            -   Separate contexts may be defined for intra-predicted and                inter-predicted CUs/TUs.            -   Separate contexts may be defined based on the minimum of                width and height of a block.    -   7. In addition to separable transforms, the MTS design may also        include non-separable transforms as transform candidates. An        example is illustrated in Table 11.

TABLE 11 Example transform candidates including non-separable transformsin addition to separable transforms in the MTS design CandidateHorizontal (H) Vertical (V) Codeword 1 IDT IDT 0 2 DCT-2 DCT-2 10 3DST-7 DST-7 110 4 DCT-8 DST-7 1110 5 DST-7 DCT-8 11110 6 Non-separableTransform 1 111110 7 Non-separable Transform 2 111111

Moreover, secondary transforms can be included in an MTS design inaddition to separable transforms. Table 12 presents an example of MTSwhere the H: DCT-8, V: DCT-8 combination is replaced by a set ofsecondary transforms.

Secondary transforms may include the aspects described in U.S.application Ser. No. 15/270,455, filed Sep. 20, 2016 and Ser. No.16/364,007 filed Mar. 25, 2019. Specifically, at the encoder side asecondary transform can be applied to a subset of primary transformcoefficients (e.g., obtained from 2-D DCT-2), where the order isreversed at the decoder (first inverse secondary transform is applied,then a primary transformation is applied).

Secondary transforms may require an additional signaling to determinethe transform selected among multiple secondary transforms asillustrated in FIG. 8 and discussed in greater detail below. Note that,if there is only a single secondary transform candidate (i.e., the setmay be only a single secondary transform), no additional signaling isrequired on top of the MTS signaling in Table 12.

For secondary transforms, transform candidates may also depend on one orcombinations of prediction mode, block-size and block-shape.

TABLE 12 Transform candidates including secondary transforms in additionto separable transforms in the MTS design Candidate Horizontal (H)Vertical (V) Codeword 1 IDT IDT 0 2 DCT-2 DCT-2 10 3 DST-7 DST-7 110 4DCT-8 DST-7 1110 5 DST-7 DCT-8 11110 6 Secondary Transforms 11111

-   -   8. Separable transforms in an MTS design may be constructed        using combinations of other type of DSTs and DCTs (e.g., DST-4        and DCT-4) in addition to IDT, DST-7, DCT-8, and DCT-2.    -   9. One or combinations of the above methods can be used for        intra predicted CUs.    -   10. One or combinations of the above methods can be used for        inter predicted CUs.    -   11. One or combinations of the above methods can be used for        both intra and inter predicted CUs.    -   12. One or combinations of the above methods can be used for        luma or chroma channels or both.

FIG. 8 is a conceptual diagram illustrating an example MTS designsupporting secondary transforms. If a secondary transform issignaled/chosen, additional signaling may be used to indicate asecondary transform among N possible secondary transforms. That is,video encoder 200 may encode a first codeword indicating a primarytransform and that a secondary transform is to be applied in addition tothe primary transform, and further encode a second codeword indicatingthe secondary transform of a set of transforms (e.g., one of the Navailable transforms depicted in FIG. 8 ). Similarly, video decoder 300may decode the first codeword and determine that the first codewordindicates a primary transform and that a secondary transform is to beapplied. Thus, video decoder 300 may further decode a second codeword inresponse to the first codeword, and use the second codeword to determinethe secondary transform. Video encoder 200 and video decoder 300 mayfurther apply both the primary and secondary transforms.

In some examples, as discussed in greater detail below, the secondarytransform may be a Low-Frequency Non-separable Transformation (LFNST).Thus, the first codeword may be referred to as an MST syntax element,and the second codeword may be referred to as an LFNST syntax element.

FIGS. 9 and 10 are conceptual diagrams illustrating the use ofLow-Frequency Non-separable Transformation (LFNST). LFNST is used inJEM-7.0 to further improve the coding efficiency of MTS, where animplementation of LFNST is based on a Hypercube-Givens Transform (HyGT),which is described in U.S. Patent Publication No. 2017/0238013, U.S.Patent Publication Nos. 2017/0094313, 2017/0238014, U.S. patentapplication Ser. No. 16/364,007, and U.S. Provisional PatentApplications 62/668,105 and 62/849,689 (describing alternative designsand further details). LFNST was previously called non-separablesecondary transform (NSST) or secondary transform, but LFNST, NSST, andsecondary transform may generally refer to the same techniques.Recently, LFNST was adopted into the draft VVC standard, as described inKoo et al., “CE6: Reduced Secondary Transform (RST) (CE6-3.1),” JointVideo Experts Team (JVET) of ITU-T SG 16 WP 3 and ISO/IEC JTC 1/SC 29/WG11, 14^(th) Meeting, Geneva, CH, 19-27 Mar. 2019, document JVET-N0193.

FIG. 9 is a conceptual diagram illustrating LFNST transforms applied byvideo encoder 200 and video decoder 300. LFNST introduces a new stagebetween separable transformation and quantization in a codec. FIG. 10 isa conceptual diagram illustrating LFNST applied to a subset ofcoefficients (at the top-left part) of an H×W block. VVC Draft 5includes the following specifications that introduce someencoder/decoder complexity with no significant coding benefit:

-   -   1) LFNST can be used with any MTS transform except the transform        skip (TS) mode,    -   2) The context model used for signaling an LFNST index depends        on an MTS index. For instance, a video coder may select a        context model used in CABAC coding (or other coding technique)        the LFNST index based on an MTS index. The context model may        indicate a probability of a first bit of the LFNST index having        a particular value.    -   3) LFNST can be used in coding chroma channels, although MTS is        normatively disabled for chroma,    -   4) LFNST applied on 4×4 and 8×8 blocks can be implemented using        a single stage (i.e., using a single non-separable transform),        yet the current implementation is based on a two-stage process.

This disclosure describes techniques that may simplify the LFNST designby addressing the above issues. The LFNST designs described in thisdisclosure may be used individually or in any combination.

In VVC Draft 5, LFNST includes 3 modes, which are signaled using LFNSTindex values 0, 1 and 2, where:

-   -   LFNST index 0 corresponds to skipping the LFNST process (e.g.,        only MTS is used),    -   LFNST indices 1 and 2 are used to determine a non-separable        transform from a set of two transforms chosen depending on a        mode and a size of a block (e.g., a CU, TU, etc.).

Based on this design, LFNST can be restricted to be used under certainconditions:

-   -   LFNST may be applied together with a predefined set of        transforms (i.e., certain MTS candidates). So, LFNST index may        be signaled if a transform from the predefined set is selected,        and the set may depend on block dimensions (width and height).        Otherwise, i.e., if a transform out of the predefined set is        chosen, LFNST index may be inferred as zero so that LFNST is        skipped (i.e., not applied).        -   The use of LFNST can be restricted based on transform type            and/or MTS index/flag and/or block dimensions.            -   LFNST can be enabled when predefined transforms types                and/or MTS indices/flags are used.                -   LFNST can be enabled if separable 2-D DCT-2 is used                    (i.e., if DCT-2 is applied horizontally and                    vertically)                -    In VVC, this corresponds to signaling an LFNST                    index if the MTS index/flag is zero (i.e., 2-D DCT-2                    is used), and the LFNST index/flag is not signaled                    and is inferred by video decoder 300 as zero if the                    MTS index/flag is different than 0.                -    In this case, the context model for coding the                    LFNST index/flag does not depend on the MTS index.            -   LFNST can be disabled for transform skip mode.                -   When transform skip is enabled, LFNST process is                    skipped and LFNST index/flag is inferred as 0.        -   Context models for coding signaling of the LFNST index may            depend on the MTS index. For each MTS index, separate            contexts can be defined for coding LFNST indices.    -   LFNST can be used for luma blocks and can be disabled for the        chroma channel. So, the LFNST index is not signaled and inferred        as 0 for the chroma channel.

Hence, in an example in accordance with one or more techniques of thisdisclosure, video encoder 200 may add to a bitstream that comprises anencoded representation of the video data, a LFNST index for a currentblock of the video data if one or more restrictions on the signaling ofthe LFNST index do not apply for the current block. Additionally, inthis example, video encoder 200 may apply a transform to residual datafor the current block to generate to generate intermediate data for thecurrent block. In this example, based on a value of the LFNST index,video encoder 200 may apply a LFNST to the intermediate data to generatetransform coefficients for the current block. Video encoder 200 mayinclude data representing the transform coefficients for the currentblock in the bitstream.

In one example in accordance with one or more techniques of thisdisclosure, video decoder 300 may obtain, from a bitstream including anencoded representation of the video data, a LFNST index for a currentblock of the video data if one or more restrictions on the signaling ofthe LFNST index do not apply for the current block. In this example,video decoder 300 may determine, based on data in the bitstream, a blockof transform coefficients. Based on a value of the LFNST index, videodecoder 300 may apply an inverse LFNST to the block of transformcoefficients to generate intermediate data for the current block. Videodecoder 300 may apply an inverse of a transform to the intermediate datafor the current block to generate residual data for the current block.In this example, video decoder 300 may reconstruct samples of thecurrent block based on the residual data for the current block.

FIGS. 11A and 11B are conceptual diagrams illustrating an exampletwo-step LFNST process implementation per the VVC test model (VTM) ofMay 30, 2019. In this example, the LFNST is applied on top of a subsetof separable transform coefficients (e.g., MTS coefficients) within thedarker-shaded subblock at the top-left region. This two-step proceduremay be unavoidable for the block shapes/sizes in FIG. 11A. However, for4×4 and 8×8 blocks, as shown in FIG. 11B, LFNST and separable transformsizes are aligned (i.e., the support of LFNST and separable transformsmay include the same coefficient locations/positions within thedarker-shaded block). In this case, this transform process can bereduced to a single-stage non-separable transform as follows:

-   -   Instead of applying a LFNST in two stages (e.g., instead of        applying LFNST with a separable transform), video encoder 200        and video decoder 300 may obtain the coefficients directly from        a non-separable transform in one stage. For example:        -   For 4×4 case, a 16-length non-separable transform is used,            which can be implemented as a matrix-vector multiplication.        -   For 8×8 case, a 64-length non-separable transform is used,            which can also be implemented as a matrix-vector            multiplication.    -   Moreover, the zero-out scheme (e.g., described in U.S.        Provisional Patent Application 62/849,689) can be used to reduce        the number of multiplications required for matrix-based        implementations.        -   In a zero-out scheme, the first K lowest-frequency            coefficients may need to be computed, and the rest of the            transform coefficients may be zeroed-out normatively (i.e.,            assumed to be zero, at both video encoder 200 and video            decoder 300).            -   The value of K may depend on the block size. For                example:                -   For 4×4 blocks, K can be 8, so the remaining 8                    coefficients are normatively zeroed out.                -   For 8×8 blocks, K can be 8, so the remaining 56                    coefficients are normatively zeroed out.                -   For 8×8 blocks, K can be 16, so the remaining 48                    coefficients are normatively zeroed out.    -   LFNST can be implemented as a single stage non-separable        transform for 4×4 and 8×8, and for other cases LFNST may be        implemented as a two-step process as described in U.S.        Provisional Patent 62/337,736.

In an example in accordance with the techniques of this disclosure,video encoder 200 may determine residual data for a first block of thevideo data. Additionally, video encoder 200 may determine residual datafor a second block of the video data. Based on a width of the firstblock being equal to a height of the first block: video encoder 200 mayapply a non-separable transform to the residual data for the first blockto generate transform coefficients for the first block; and include, ina bitstream that includes an encoded representation of the video data,data representing the transform coefficients for the first block. Inthis example, based on a width of the second block not being equal to aheight of the second block, video encoder 200 may apply a transform tothe residual data for the second block to generate intermediate data forthe second block; apply a LFNST to the intermediate data for the secondblock to generate transform coefficients for the second block; andinclude, in the bitstream, data representing the transform coefficientsfor the second block.

In another example in accordance with the techniques of this disclosure,video decoder 300 may determine, based on first data in a bitstream thatincludes an encoded representation of the video data, transformcoefficients for a first block of the video. Additionally, video decoder300 may determine, based on second data in the bitstream, transformcoefficients for a second block of the video data. Based on a width ofthe first block being equal to a height of the first block, videodecoder 300 may apply an inverse of a non-separable transform to thetransform coefficients for the first block to generate residual data forthe first block; and reconstruct samples of the first block based on theresidual data for the first block. In this example, based on a width ofthe second block not being equal to a height of the second block, videodecoder 300 may apply an inverse transform to the transform coefficientsfor the second block to generate intermediate data for the second block;apply an inverse of a LFNST to the intermediate data for the secondblock to generate residual data for the second block; and reconstructsamples of the second block based on the residual data for the secondblock.

FIG. 12 is a block diagram illustrating an example video encoder 200that may perform the techniques of this disclosure. FIG. 12 is providedfor purposes of explanation and should not be considered limiting of thetechniques as broadly exemplified and described in this disclosure. Forpurposes of explanation, this disclosure describes video encoder 200 inthe context of video coding standards such as the HEVC video codingstandard and the H.266/VVC video coding standard in development.However, the techniques of this disclosure are not limited to thesevideo coding standards, and are applicable generally to video encodingand decoding.

In the example of FIG. 12 , video encoder 200 includes video data memory230, mode selection unit 202, residual generation unit 204, transformprocessing unit 206, quantization unit 208, inverse quantization unit210, inverse transform processing unit 212, reconstruction unit 214,filter unit 216, decoded picture buffer (DPB) 218, and entropy encodingunit 220. FIG. 12 may further include a transform bank from whichtransform processing unit 206 and inverse transform processing unit 212select transforms according to the techniques of this disclosure, asshown in FIG. 4 above. Likewise, as shown in FIG. 4 , transformprocessing unit 206 may provide an indication of a selected transform toentropy encoding unit 220, which may encode data according to thetechniques of this disclosure representing which of a variety oftransforms for an MTS scheme is selected for a current block of videodata.

Video data memory 230 may store video data to be encoded by thecomponents of video encoder 200. Video encoder 200 may receive the videodata stored in video data memory 230 from, for example, video source 104(FIG. 1 ). DPB 218 may act as a reference picture memory that storesreference video data for use in prediction of subsequent video data byvideo encoder 200. Video data memory 230 and DPB 218 may be formed byany of a variety of memory devices, such as dynamic random access memory(DRAM), including synchronous DRAM (SDRAM), magnetoresistive RAM (MRAM),resistive RAM (RRAM), or other types of memory devices. Video datamemory 230 and DPB 218 may be provided by the same memory device orseparate memory devices. In various examples, video data memory 230 maybe on-chip with other components of video encoder 200, as illustrated,or off-chip relative to those components.

In this disclosure, reference to video data memory 230 should not beinterpreted as being limited to memory internal to video encoder 200,unless specifically described as such, or memory external to videoencoder 200, unless specifically described as such. Rather, reference tovideo data memory 230 should be understood as reference memory thatstores video data that video encoder 200 receives for encoding (e.g.,video data for a current block that is to be encoded). Memory 106 ofFIG. 1 may also provide temporary storage of outputs from the variousunits of video encoder 200.

The various units of FIG. 12 are illustrated to assist withunderstanding the operations performed by video encoder 200. The unitsmay be implemented as fixed-function circuits, programmable circuits, ora combination thereof. Fixed-function circuits refer to circuits thatprovide particular functionality, and are preset on the operations thatcan be performed. Programmable circuits refer to circuits that canprogrammed to perform various tasks, and provide flexible functionalityin the operations that can be performed. For instance, programmablecircuits may execute software or firmware that cause the programmablecircuits to operate in the manner defined by instructions of thesoftware or firmware. Fixed-function circuits may execute softwareinstructions (e.g., to receive parameters or output parameters), but thetypes of operations that the fixed-function circuits perform aregenerally immutable. In some examples, the one or more of the units maybe distinct circuit blocks (fixed-function or programmable), and in someexamples, the one or more units may be integrated circuits.

Video encoder 200 may include arithmetic logic units (ALUs), elementaryfunction units (EFUs), digital circuits, analog circuits, and/orprogrammable cores, formed from programmable circuits. In examples wherethe operations of video encoder 200 are performed using softwareexecuted by the programmable circuits, memory 106 (FIG. 1 ) may storethe object code of the software that video encoder 200 receives andexecutes, or another memory within video encoder 200 (not shown) maystore such instructions.

Video data memory 230 is configured to store received video data. Videoencoder 200 may retrieve a picture of the video data from video datamemory 230 and provide the video data to residual generation unit 204and mode selection unit 202. Video data in video data memory 230 may beraw video data that is to be encoded.

Mode selection unit 202 includes a motion estimation unit 222, motioncompensation unit 224, and an intra-prediction unit 226. Mode selectionunit 202 may include additional functional units to perform videoprediction in accordance with other prediction modes. As examples, modeselection unit 202 may include a palette unit, an intra-block copy unit(which may be part of motion estimation unit 222 and/or motioncompensation unit 224), an affine unit, a linear model (LM) unit, or thelike.

Mode selection unit 202 generally coordinates multiple encoding passesto test combinations of encoding parameters and resultingrate-distortion values for such combinations. The encoding parametersmay include partitioning of CTUs into CUs, prediction modes for the CUs,transform types for residual data of the CUs, quantization parametersfor residual data of the CUs, and so on. Mode selection unit 202 mayultimately select the combination of encoding parameters havingrate-distortion values that are better than the other testedcombinations.

Video encoder 200 may partition a picture retrieved from video datamemory 230 into a series of CTUs, and encapsulate one or more CTUswithin a slice. Mode selection unit 202 may partition a CTU of thepicture in accordance with a tree structure, such as the QTBT structureor the quad-tree structure of HEVC described above. As described above,video encoder 200 may form one or more CUs from partitioning a CTUaccording to the tree structure. Such a CU may also be referred togenerally as a “video block” or “block.”

In general, mode selection unit 202 also controls the components thereof(e.g., motion estimation unit 222, motion compensation unit 224, andintra-prediction unit 226) to generate a prediction block for a currentblock (e.g., a current CU, or in HEVC, the overlapping portion of a PUand a TU). For inter-prediction of a current block, motion estimationunit 222 may perform a motion search to identify one or more closelymatching reference blocks in one or more reference pictures (e.g., oneor more previously coded pictures stored in DPB 218). In particular,motion estimation unit 222 may calculate a value representative of howsimilar a potential reference block is to the current block, e.g.,according to sum of absolute difference (SAD), sum of squareddifferences (SSD), mean absolute difference (MAD), mean squareddifferences (MSD), or the like. Motion estimation unit 222 may generallyperform these calculations using sample-by-sample differences betweenthe current block and the reference block being considered. Motionestimation unit 222 may identify a reference block having a lowest valueresulting from these calculations, indicating a reference block thatmost closely matches the current block.

Motion estimation unit 222 may form one or more motion vectors (MVs)that defines the positions of the reference blocks in the referencepictures relative to the position of the current block in a currentpicture. Motion estimation unit 222 may then provide the motion vectorsto motion compensation unit 224. For example, for uni-directionalinter-prediction, motion estimation unit 222 may provide a single motionvector, whereas for bi-directional inter-prediction, motion estimationunit 222 may provide two motion vectors. Motion compensation unit 224may then generate a prediction block using the motion vectors. Forexample, motion compensation unit 224 may retrieve data of the referenceblock using the motion vector. As another example, if the motion vectorhas fractional sample precision, motion compensation unit 224 mayinterpolate values for the prediction block according to one or moreinterpolation filters. Moreover, for bi-directional inter-prediction,motion compensation unit 224 may retrieve data for two reference blocksidentified by respective motion vectors and combine the retrieved data,e.g., through sample-by-sample averaging or weighted averaging.

As another example, for intra-prediction, or intra-prediction coding,intra-prediction unit 226 may generate the prediction block from samplesneighboring the current block. For example, for directional modes,intra-prediction unit 226 may generally mathematically combine values ofneighboring samples and populate these calculated values in the defineddirection across the current block to produce the prediction block. Asanother example, for DC mode, intra-prediction unit 226 may calculate anaverage of the neighboring samples to the current block and generate theprediction block to include this resulting average for each sample ofthe prediction block.

Mode selection unit 202 provides the prediction block to residualgeneration unit 204. Residual generation unit 204 receives a raw,uncoded version of the current block from video data memory 230 and theprediction block from mode selection unit 202. Residual generation unit204 calculates sample-by-sample differences between the current blockand the prediction block. The resulting sample-by-sample differencesdefine a residual block for the current block. In some examples,residual generation unit 204 may also determine differences betweensample values in the residual block to generate a residual block usingresidual differential pulse code modulation (RDPCM). In some examples,residual generation unit 204 may be formed using one or more subtractorcircuits that perform binary subtraction.

In examples where mode selection unit 202 partitions CUs into PUs, eachPU may be associated with a luma prediction unit and correspondingchroma prediction units. Video encoder 200 and video decoder 300 maysupport PUs having various sizes. As indicated above, the size of a CUmay refer to the size of the luma coding block of the CU and the size ofa PU may refer to the size of a luma prediction unit of the PU. Assumingthat the size of a particular CU is 2N×2N, video encoder 200 may supportPU sizes of 2N×2N or N×N for intra prediction, and symmetric PU sizes of2N×2N, 2N×N, N×2N, N×N, or similar for inter prediction. Video encoder200 and video decoder 300 may also support asymmetric partitioning forPU sizes of 2N×nU, 2N×nD, nL×2N, and nR×2N for inter prediction.

In examples where mode selection unit does not further partition a CUinto PUs, each CU may be associated with a luma coding block andcorresponding chroma coding blocks. As above, the size of a CU may referto the size of the luma coding block of the CU. The video encoder 200and video decoder 300 may support CU sizes of 2N×2N, 2N×N, or N×2N.

For other video coding techniques such as an intra-block copy modecoding, an affine-mode coding, and linear model (LM) mode coding, as fewexamples, mode selection unit 202, via respective units associated withthe coding techniques, generates a prediction block for the currentblock being encoded. In some examples, such as palette mode coding, modeselection unit 202 may not generate a prediction block, and insteadgenerate syntax elements that indicate the manner in which toreconstruct the block based on a selected palette. In such modes, modeselection unit 202 may provide these syntax elements to entropy encodingunit 220 to be encoded.

As described above, residual generation unit 204 receives the video datafor the current block and the corresponding prediction block. Residualgeneration unit 204 then generates a residual block for the currentblock. To generate the residual block, residual generation unit 204calculates sample-by-sample differences between the prediction block andthe current block. Thus,

Transform processing unit 206 applies one or more transforms to theresidual block to generate a block of transform coefficients (referredto herein as a “transform coefficient block”). Transform processing unit206 may apply various transforms to a residual block to form thetransform coefficient block. For example, transform processing unit 206may apply a discrete cosine transform (DCT), a directional transform, aKarhunen-Loeve transform (KLT), or a conceptually similar transform to aresidual block. In some examples, transform processing unit 206 mayperform multiple transforms to a residual block, e.g., a primarytransform and a secondary transform, such as a rotational transform. Insome examples, transform processing unit 206 does not apply transformsto a residual block.

In accordance with the techniques of this disclosure, transformprocessing unit 206 may select a transform scheme (e.g., an MTS scheme)including both a primary transform and a secondary transform. Theprimary transform may be a separable transform including a horizontaltransform and a vertical transform, such as one of a variety of DCTsand/or DSTs. The secondary transform may be an LFNST. Transformprocessing unit 206 may additionally provide an indication of theselected transform scheme and, if the selected transform scheme includesa secondary transform, an indication of the selected secondary transformto entropy encoding unit 220. Entropy encoding unit 220 may, in turn,encode a first codeword representing the selected transform scheme(which may also indicate whether the selected transform scheme includesa secondary transform). If the selected transform scheme includes asecondary transform, such as an LFNST, entropy encoding unit 220 mayfurther encode a second codeword representing the selected secondarytransform. Video encoder 200 may determine that the selected transformscheme includes the secondary transform if, for example, the primarytransform includes a DCT-2 horizontal transform and a DCT-2 verticaltransform, as discussed above. Furthermore, transform processing unit206 may apply the primary transform to the residual block. If theselected transform scheme includes the secondary transform, transformprocessing unit 206 may also apply the secondary transform following theprimary transform.

Quantization unit 208 may quantize the transform coefficients in atransform coefficient block, to produce a quantized transformcoefficient block. Quantization unit 208 may quantize transformcoefficients of a transform coefficient block according to aquantization parameter (QP) value associated with the current block.Video encoder 200 (e.g., via mode selection unit 202) may adjust thedegree of quantization applied to the coefficient blocks associated withthe current block by adjusting the QP value associated with the CU.Quantization may introduce loss of information, and thus, quantizedtransform coefficients may have lower precision than the originaltransform coefficients produced by transform processing unit 206.

Inverse quantization unit 210 and inverse transform processing unit 212may apply inverse quantization and inverse transforms to a quantizedtransform coefficient block, respectively, to reconstruct a residualblock from the transform coefficient block. According to the techniquesof this disclosure, inverse transform processing unit 212 may apply aninverse secondary transform and then an inverse primary transform to thetransform coefficients. Reconstruction unit 214 may produce areconstructed block corresponding to the current block (albeitpotentially with some degree of distortion) based on the reconstructedresidual block and a prediction block generated by mode selection unit202. For example, reconstruction unit 214 may add samples of thereconstructed residual block to corresponding samples from theprediction block generated by mode selection unit 202 to produce thereconstructed block.

Filter unit 216 may perform one or more filter operations onreconstructed blocks. For example, filter unit 216 may performdeblocking operations to reduce blockiness artifacts along edges of CUs.Operations of filter unit 216 may be skipped, in some examples.

Video encoder 200 stores reconstructed blocks in DPB 218. For instance,in examples where operations of filter unit 216 are not needed,reconstruction unit 214 may store reconstructed blocks to DPB 218. Inexamples where operations of filter unit 216 are needed, filter unit 216may store the filtered reconstructed blocks to DPB 218. Motionestimation unit 222 and motion compensation unit 224 may retrieve areference picture from DPB 218, formed from the reconstructed (andpotentially filtered) blocks, to inter-predict blocks of subsequentlyencoded pictures. In addition, intra-prediction unit 226 may usereconstructed blocks in DPB 218 of a current picture to intra-predictother blocks in the current picture.

In general, entropy encoding unit 220 may entropy encode syntax elementsreceived from other functional components of video encoder 200. Forexample, entropy encoding unit 220 may entropy encode quantizedtransform coefficient blocks from quantization unit 208. As anotherexample, entropy encoding unit 220 may entropy encode prediction syntaxelements (e.g., motion information for inter-prediction or intra-modeinformation for intra-prediction) from mode selection unit 202. Entropyencoding unit 220 may perform one or more entropy encoding operations onthe syntax elements, which are another example of video data, togenerate entropy-encoded data. For example, entropy encoding unit 220may perform a context-adaptive variable length coding (CAVLC) operation,a CABAC operation, a variable-to-variable (V2V) length coding operation,a syntax-based context-adaptive binary arithmetic coding (SBAC)operation, a Probability Interval Partitioning Entropy (PIPE) codingoperation, an Exponential-Golomb encoding operation, or another type ofentropy encoding operation on the data. In some examples, entropyencoding unit 220 may operate in bypass mode where syntax elements arenot entropy encoded.

Video encoder 200 may output a bitstream that includes the entropyencoded syntax elements needed to reconstruct blocks of a slice orpicture. In particular, entropy encoding unit 220 may output thebitstream

The operations described above are described with respect to a block.Such description should be understood as being operations for a lumacoding block and/or chroma coding blocks. As described above, in someexamples, the luma coding block and chroma coding blocks are luma andchroma components of a CU. In some examples, the luma coding block andthe chroma coding blocks are luma and chroma components of a PU.

In some examples, operations performed with respect to a luma codingblock need not be repeated for the chroma coding blocks. As one example,operations to identify a motion vector (MV) and reference picture for aluma coding block need not be repeated for identifying a MV andreference picture for the chroma blocks. Rather, the MV for the lumacoding block may be scaled to determine the MV for the chroma blocks,and the reference picture may be the same. As another example, theintra-prediction process may be the same for the luma coding blocks andthe chroma coding blocks.

Video encoder 200 represents an example of a device configured to encodevideo data including a memory configured to store video data, and one ormore processing units implemented in circuitry and configured to code afirst codeword representing a selected transform scheme of a set oftransform candidates of a multiple transform selection (MTS) scheme fora current block of video data, the selected transform scheme being asecondary transform of a set of available secondary transforms to beapplied in addition to a primary transform; code a second codewordrepresenting the secondary transform from the set of available secondarytransforms; and apply the primary transform and the secondary transformduring coding of residual data for the current block.

FIG. 13 is a block diagram illustrating an example video decoder 300that may perform the techniques of this disclosure. FIG. 13 is providedfor purposes of explanation and is not limiting on the techniques asbroadly exemplified and described in this disclosure. For purposes ofexplanation, this disclosure describes video decoder 300 is describedaccording to the techniques of VVC and HEVC. However, the techniques ofthis disclosure may be performed by video coding devices that areconfigured to other video coding standards.

In the example of FIG. 13 , video decoder 300 includes coded picturebuffer (CPB) memory 320, entropy decoding unit 302, predictionprocessing unit 304, inverse quantization unit 306, inverse transformprocessing unit 308, reconstruction unit 310, filter unit 312, anddecoded picture buffer (DPB) 314. FIG. 13 may further include atransform bank from which inverse transform processing unit 308 selecttransforms according to the techniques of this disclosure, as shown inFIG. 4 above. Likewise, reciprocal to the techniques shown in FIG. 4 ,entropy decoding unit 302 may decode data according to the techniques ofthis disclosure representing which of a variety of transforms for an MTSscheme is selected for a current block of video data and provide anindication of the transform to inverse transform processing unit 308.

Prediction processing unit 304 includes motion compensation unit 316 andintra-prediction unit 318. Prediction processing unit 304 may includeaddition units to perform prediction in accordance with other predictionmodes. As examples, prediction processing unit 304 may include a paletteunit, an intra-block copy unit (which may form part of motioncompensation unit 316), an affine unit, a linear model (LM) unit, or thelike. In other examples, video decoder 300 may include more, fewer, ordifferent functional components.

CPB memory 320 may store video data, such as an encoded video bitstream,to be decoded by the components of video decoder 300. The video datastored in CPB memory 320 may be obtained, for example, fromcomputer-readable medium 110 (FIG. 1 ). CPB memory 320 may include a CPBthat stores encoded video data (e.g., syntax elements) from an encodedvideo bitstream. Also, CPB memory 320 may store video data other thansyntax elements of a coded picture, such as temporary data representingoutputs from the various units of video decoder 300. DPB 314 generallystores decoded pictures, which video decoder 300 may output and/or useas reference video data when decoding subsequent data or pictures of theencoded video bitstream. CPB memory 320 and DPB 314 may be formed by anyof a variety of memory devices, such as dynamic random access memory(DRAM), including synchronous DRAM (SDRAM), magnetoresistive RAM (MRAM),resistive RAM (RRAM), or other types of memory devices. CPB memory 320and DPB 314 may be provided by the same memory device or separate memorydevices. In various examples, CPB memory 320 may be on-chip with othercomponents of video decoder 300, or off-chip relative to thosecomponents.

Additionally or alternatively, in some examples, video decoder 300 mayretrieve coded video data from memory 120 (FIG. 1 ). That is, memory 120may store data as discussed above with CPB memory 320. Likewise, memory120 may store instructions to be executed by video decoder 300, whensome or all of the functionality of video decoder 300 is implemented insoftware to executed by processing circuitry of video decoder 300.

The various units shown in FIG. 13 are illustrated to assist withunderstanding the operations performed by video decoder 300. The unitsmay be implemented as fixed-function circuits, programmable circuits, ora combination thereof. Similar to FIG. 12 , fixed-function circuitsrefer to circuits that provide particular functionality, and are preseton the operations that can be performed. Programmable circuits refer tocircuits that can programmed to perform various tasks, and provideflexible functionality in the operations that can be performed. Forinstance, programmable circuits may execute software or firmware thatcause the programmable circuits to operate in the manner defined byinstructions of the software or firmware. Fixed-function circuits mayexecute software instructions (e.g., to receive parameters or outputparameters), but the types of operations that the fixed-functioncircuits perform are generally immutable. In some examples, the one ormore of the units may be distinct circuit blocks (fixed-function orprogrammable), and in some examples, the one or more units may beintegrated circuits.

Video decoder 300 may include ALUs, EFUs, digital circuits, analogcircuits, and/or programmable cores formed from programmable circuits.In examples where the operations of video decoder 300 are performed bysoftware executing on the programmable circuits, on-chip or off-chipmemory may store instructions (e.g., object code) of the software thatvideo decoder 300 receives and executes.

Entropy decoding unit 302 may receive encoded video data from the CPBand entropy decode the video data to reproduce syntax elements.Prediction processing unit 304, inverse quantization unit 306, inversetransform processing unit 308, reconstruction unit 310, and filter unit312 may generate decoded video data based on the syntax elementsextracted from the bitstream.

According to the techniques of this disclosure, entropy decoding unit302 may decode a first codeword representing a transform scheme to beapplied to decoded transform coefficients for a current block of videodata. Entropy decoding unit 302 may further determine whether theselected transform scheme includes a secondary transform (e.g., anLFNST) to be applied in addition to a primary transform. For example, ifthe primary transform includes a DCT-2 horizontal transform and a DCT-2vertical transform, entropy decoding unit 302 may determine that thesecondary transform is also to be applied. Moreover, in response todetermining that the secondary transform is to be applied, entropydecoding unit 302 may also decode a second codeword representing thesecondary transform of a set of available secondary transforms.

In general, video decoder 300 reconstructs a picture on a block-by-blockbasis. Video decoder 300 may perform a reconstruction operation on eachblock individually (where the block currently being reconstructed, i.e.,decoded, may be referred to as a “current block”).

Entropy decoding unit 302 may entropy decode syntax elements definingquantized transform coefficients of a quantized transform coefficientblock, as well as transform information, such as a quantizationparameter (QP) and/or transform mode indication(s). Inverse quantizationunit 306 may use the QP associated with the quantized transformcoefficient block to determine a degree of quantization and, likewise, adegree of inverse quantization for inverse quantization unit 306 toapply. Inverse quantization unit 306 may, for example, perform a bitwiseleft-shift operation to inverse quantize the quantized transformcoefficients. Inverse quantization unit 306 may thereby form a transformcoefficient block including transform coefficients.

After inverse quantization unit 306 forms the transform coefficientblock, inverse transform processing unit 308 may apply one or moreinverse transforms to the transform coefficient block to generate aresidual block associated with the current block. For example, inversetransform processing unit 308 may apply an inverse DCT, an inverseinteger transform, an inverse Karhunen-Loeve transform (KLT), an inverserotational transform, an inverse directional transform, or anotherinverse transform to the coefficient block. If the transform schemeincludes a secondary transform, inverse quantization unit 306 may applythe secondary transform prior to applying a primary transform.

Furthermore, prediction processing unit 304 generates a prediction blockaccording to prediction information syntax elements that were entropydecoded by entropy decoding unit 302. For example, if the predictioninformation syntax elements indicate that the current block isinter-predicted, motion compensation unit 316 may generate theprediction block. In this case, the prediction information syntaxelements may indicate a reference picture in DPB 314 from which toretrieve a reference block, as well as a motion vector identifying alocation of the reference block in the reference picture relative to thelocation of the current block in the current picture. Motioncompensation unit 316 may generally perform the inter-prediction processin a manner that is substantially similar to that described with respectto motion compensation unit 224 (FIG. 12 ).

As another example, if the prediction information syntax elementsindicate that the current block is intra-predicted, intra-predictionunit 318 may generate the prediction block according to anintra-prediction mode indicated by the prediction information syntaxelements. Again, intra-prediction unit 318 may generally perform theintra-prediction process in a manner that is substantially similar tothat described with respect to intra-prediction unit 226 (FIG. 12 ).Intra-prediction unit 318 may retrieve data of neighboring samples tothe current block from DPB 314.

Reconstruction unit 310 may reconstruct the current block using theprediction block and the residual block. For example, reconstructionunit 310 may add samples of the residual block to corresponding samplesof the prediction block to reconstruct the current block.

Filter unit 312 may perform one or more filter operations onreconstructed blocks. For example, filter unit 312 may performdeblocking operations to reduce blockiness artifacts along edges of thereconstructed blocks. Operations of filter unit 312 are not necessarilyperformed in all examples.

Video decoder 300 may store the reconstructed blocks in DPB 314. Asdiscussed above, DPB 314 may provide reference information, such assamples of a current picture for intra-prediction and previously decodedpictures for subsequent motion compensation, to prediction processingunit 304. Moreover, video decoder 300 may output decoded pictures fromDPB for subsequent presentation on a display device, such as displaydevice 118 of FIG. 1 .

Video decoder 300 represents an example of a video decoding deviceincluding a memory configured to store video data, and one or moreprocessing units implemented in circuitry and configured to code a firstcodeword representing a selected transform scheme of a set of transformcandidates of a multiple transform selection (MTS) scheme for a currentblock of video data, the selected transform scheme being a secondarytransform of a set of available secondary transforms to be applied inaddition to a primary transform; code a second codeword representing thesecondary transform from the set of available secondary transforms; andapply the primary transform and the secondary transform during coding ofresidual data for the current block.

FIG. 14 is a flowchart illustrating an example method for encoding acurrent block according to the techniques of this disclosure. Thecurrent block may comprise a current CU. Although described with respectto video encoder 200 (FIGS. 1 and 12 ), it should be understood thatother devices may be configured to perform a method similar to that ofFIG. 14 .

In this example, video encoder 200 initially predicts the current block(350). For example, video encoder 200 may form a prediction block forthe current block. Video encoder 200 may then calculate a residual blockfor the current block (352). To calculate the residual block, videoencoder 200 may calculate a difference between the original, uncodedblock and the prediction block for the current block. Video encoder 200may then select a transform and use the selected transform and quantizecoefficients of the residual block (354). The selected transform mayinclude a primary transform and/or a secondary transform, such as anLFNST. Video encoder 200 may apply either or both of a primary transformand/or the secondary transform according to the selected transform.

Next, video encoder 200 may scan the quantized transform coefficients ofthe residual block (356). During the scan, or following the scan, videoencoder 200 may entropy encode the coefficients, as well as datarepresenting the selected transform (358). For example, video encoder200 may entropy encode data representing the transform using any of thevarious techniques of this disclosure as discussed above. Video encoder200 may encode the coefficients using CAVLC or CABAC. In particular,video encoder 200 may select a transform scheme according to thetechniques of this disclosure and entropy encode a codeword representingthe selected transform according to any of the techniques of thisdisclosure. If the selected transform scheme includes a secondarytransform, video encoder 200 may further encode a second codewordrepresenting the secondary transform from a set of available secondarytransforms, e.g., as discussed above with respect to FIG. 8 . Videoencoder 200 may then output the entropy encoded data representing thetransform(s) and coefficients of the block (360).

In this manner, the method of FIG. 14 represents an example of a methodof encoding video data, the method including coding a first codewordrepresenting a selected transform scheme of a set of transformcandidates of a multiple transform selection (MTS) scheme for a currentblock of video data, the selected transform scheme being a secondarytransform of a set of available secondary transforms to be applied inaddition to a primary transform; coding a second codeword representingthe secondary transform from the set of available secondary transforms;and applying the primary transform and the secondary transform duringcoding of residual data for the current block.

FIG. 15 is a flowchart illustrating an example method for decoding acurrent block of video data according to the techniques of thisdisclosure. The current block may comprise a current CU. Althoughdescribed with respect to video decoder 300 (FIGS. 1 and 13 ), it shouldbe understood that other devices may be configured to perform a methodsimilar to that of FIG. 15 .

Video decoder 300 may receive entropy coded data for the current block,such as entropy coded prediction information and entropy coded data forcoefficients of a residual block corresponding to the current block(370). Video decoder 300 may entropy decode the entropy coded data todetermine prediction information for the current block, a transform forthe current block, and to reproduce coefficients of the residual block(372). Video decoder 300 may entropy decode the transform informationaccording to any of the various techniques of this disclosure. Videodecoder 300 may predict the current block (374), e.g., using an intra-or inter-prediction mode as indicated by the prediction information forthe current block, to calculate a prediction block for the currentblock. Video decoder 300 may then inverse scan the reproducedcoefficients (376), to create a block of quantized transformcoefficients. Video decoder 300 may then inverse quantize and inversetransform the coefficients using the indicated transform to produce aresidual block (378). For example, video decoder 300 may decode acodeword representing a transform to be applied according to any of thetechniques of this disclosure. Video decoder 300 may ultimately decodethe current block by combining the prediction block and the residualblock (380).

In this manner, the method of FIG. 15 represents an example of a methodof decoding video data, the method including coding a first codewordrepresenting a selected transform scheme of a set of transformcandidates of a multiple transform selection (MTS) scheme for a currentblock of video data, the selected transform scheme being a secondarytransform of a set of available secondary transforms to be applied inaddition to a primary transform; coding a second codeword representingthe secondary transform from the set of available secondary transforms;and applying the primary transform and the secondary transform duringcoding of residual data for the current block.

FIG. 16 is a flowchart illustrating an example video encoding method inaccordance with the techniques of this disclosure. For purposes ofexample, the method of FIG. 16 is explained with respect to videoencoder 200 of FIGS. 1 and 12 , although it should be understood thatother video encoders may be configured to perform this or a similarmethod.

Initially, video encoder 200 may select a transform scheme including aprimary and a secondary transform (400). Mode selection unit 202 mayalso select the secondary transform from a set of available secondarytransforms (402). For example, mode selection unit 202 may cause thevarious components of video encoder 200 to perform various encodingpasses, including testing of various transform schemes. Mode selectionunit 202 may calculate rate-distortion metrics and determine that theselected transform scheme, including the primary and the selectedsecondary transform, yields the best tested rate-distortioncharacteristics.

Video encoder 200 may then encode a first codeword representing theselected transform scheme (404). Additionally, video encoder 200 mayencode a second codeword representing the selected secondary transformscheme (406). In particular, entropy encoding unit 220 may entropyencode the first and second codewords.

Video encoder 200 may then apply the primary transform to a residualblock (408). In particular, transform processing unit 206 may apply theprimary transform to the residual block, producing a transform block oftransform coefficients. Video encoder 200 (in particular, transformprocessing unit 206) may also apply the secondary transform to thetransform block (410).

In this manner, the method of FIG. 16 represents an example of a methodof encoding video data, the method including coding a first codewordrepresenting a selected transform scheme of a set of transformcandidates of a multiple transform selection (MTS) scheme for a currentblock of video data, the selected transform scheme being a secondarytransform of a set of available secondary transforms to be applied inaddition to a primary transform; coding a second codeword representingthe secondary transform from the set of available secondary transforms;and applying the primary transform and the secondary transform duringcoding of residual data for the current block.

FIG. 17 is a flowchart illustrating an example video decoding method inaccordance with the techniques of this disclosure. For purposes ofexample, the method of FIG. 17 is explained with respect to videodecoder 300 of FIGS. 1 and 13 , although it should be understood thatother video encoders may be configured to perform this or a similarmethod.

Video decoder 300 may initially decode a first codeword representing atransform scheme that includes both a primary transform and a secondarytransform (420). In particular, entropy decoding unit 302 may entropydecode the first codeword. Entropy decoding unit 302 of video decoder300 may also entropy decode a second codeword representing the secondarytransform in a set of available secondary transforms (422). For example,the second codeword may act as an index into the set of availablesecondary transforms.

Video decoder 300 may then apply the secondary transform to decodedtransform coefficients of a transform block (424) to produce anintermediate transform block. Video decoder 300 may also apply theprimary transform to the intermediate transform block to reproduce aresidual block (426). In particular, inverse transform processing unit308 may apply the secondary and primary transforms.

In this manner, the method of FIG. 17 represents an example of a methodof decoding video data, the method including coding a first codewordrepresenting a selected transform scheme of a set of transformcandidates of a multiple transform selection (MTS) scheme for a currentblock of video data, the selected transform scheme being a secondarytransform of a set of available secondary transforms to be applied inaddition to a primary transform; coding a second codeword representingthe secondary transform from the set of available secondary transforms;and applying the primary transform and the secondary transform duringcoding of residual data for the current block.

It is to be recognized that depending on the example, certain acts orevents of any of the techniques described herein can be performed in adifferent sequence, may be added, merged, or left out altogether (e.g.,not all described acts or events are necessary for the practice of thetechniques). Moreover, in certain examples, acts or events may beperformed concurrently, e.g., through multi-threaded processing,interrupt processing, or multiple processors, rather than sequentially.

In one or more examples, the functions described may be implemented inhardware, software, firmware, or any combination thereof. If implementedin software, the functions may be stored on or transmitted over as oneor more instructions or code on a computer-readable medium and executedby a hardware-based processing unit. Computer-readable media may includecomputer-readable storage media, which corresponds to a tangible mediumsuch as data storage media, or communication media including any mediumthat facilitates transfer of a computer program from one place toanother, e.g., according to a communication protocol. In this manner,computer-readable media generally may correspond to (1) tangiblecomputer-readable storage media which is non-transitory or (2) acommunication medium such as a signal or carrier wave. Data storagemedia may be any available media that can be accessed by one or morecomputers or one or more processors to retrieve instructions, codeand/or data structures for implementation of the techniques described inthis disclosure. A computer program product may include acomputer-readable medium.

By way of example, and not limitation, such computer-readable storagemedia can comprise RAM, ROM, EEPROM, CD-ROM or other optical diskstorage, magnetic disk storage, or other magnetic storage devices, flashmemory, or any other medium that can be used to store desired programcode in the form of instructions or data structures and that can beaccessed by a computer. Also, any connection is properly termed acomputer-readable medium. For example, if instructions are transmittedfrom a website, server, or other remote source using a coaxial cable,fiber optic cable, twisted pair, digital subscriber line (DSL), orwireless technologies such as infrared, radio, and microwave, then thecoaxial cable, fiber optic cable, twisted pair, DSL, or wirelesstechnologies such as infrared, radio, and microwave are included in thedefinition of medium. It should be understood, however, thatcomputer-readable storage media and data storage media do not includeconnections, carrier waves, signals, or other transitory media, but areinstead directed to non-transitory, tangible storage media. Disk anddisc, as used herein, includes compact disc (CD), laser disc, opticaldisc, digital versatile disc (DVD), floppy disk and Blu-ray disc, wheredisks usually reproduce data magnetically, while discs reproduce dataoptically with lasers. Combinations of the above should also be includedwithin the scope of computer-readable media.

Instructions may be executed by one or more processors, such as one ormore digital signal processors (DSPs), general purpose microprocessors,application specific integrated circuits (ASICs), field programmablegate arrays (FPGAs), or other equivalent integrated or discrete logiccircuitry. Accordingly, the term “processor,” as used herein may referto any of the foregoing structure or any other structure suitable forimplementation of the techniques described herein. In addition, in someaspects, the functionality described herein may be provided withindedicated hardware and/or software modules configured for encoding anddecoding, or incorporated in a combined codec. Also, the techniquescould be fully implemented in one or more circuits or logic elements.

The techniques of this disclosure may be implemented in a wide varietyof devices or apparatuses, including a wireless handset, an integratedcircuit (IC) or a set of ICs (e.g., a chip set). Various components,modules, or units are described in this disclosure to emphasizefunctional aspects of devices configured to perform the disclosedtechniques, but do not necessarily require realization by differenthardware units. Rather, as described above, various units may becombined in a codec hardware unit or provided by a collection ofinteroperative hardware units, including one or more processors asdescribed above, in conjunction with suitable software and/or firmware.

Various examples have been described. These and other examples arewithin the scope of the following claims.

What is claimed is:
 1. A method of transforming a block of video data,the method comprising: coding a value for a low frequency non-separabletransform (LFNST) index (LFNST_idx) syntax element for a current blockof video data, the value for the LFNST_idx syntax element being non-zeroand indicating a secondary transform for the current block of videodata; determining that a multiple transform selection (MTS) scheme forthe current block of video data indicates a discrete cosine transform 2(DCT-2) primary transform for the current block of video data; andapplying the DCT-2 primary transform and the secondary transform duringcoding of residual data for the current block of video data.
 2. Themethod of claim 1, wherein determining that the MTS scheme for thecurrent block of video data indicates the DCT-2 primary transform forthe current block of video data comprises determining that an MTS_idxsyntax element has a value of zero.
 3. The method of claim 2, whereincoding the value for the LFNST_idx syntax element comprisescontext-adaptive binary arithmetic coding (CABAC) coding the value forthe LFNST_idx syntax element, including determining a context for CABACcoding the value for the LFNST_idx syntax element without using thevalue of the MTS_idx syntax element.
 4. The method of claim 1, whereincoding the value for the LFNST_idx syntax element comprises decoding thevalue for the LFNST_idx syntax element; and wherein applying the DCT-2primary transform and the secondary transform comprises: applying thesecondary transform to decoded transform coefficients to produceintermediate transform coefficients; and applying the DCT-2 primarytransform to the intermediate transform coefficients to produce aresidual block for the current block of video data.
 5. The method ofclaim 1, wherein coding the value for the LFNST_idx syntax elementcomprises encoding the value for the LFNST_idx syntax element; andwherein applying the DCT-2 primary transform and the secondary transformcomprises: applying the DCT-2 primary transform to a residual block forthe current block of video data to generate intermediate transformcoefficients; and applying the secondary transform to the intermediatetransform coefficients.
 6. A device for transforming a block of videodata, the device comprising: a memory configured to store video data;and one or more processors implemented in circuitry and configured to:code a value for a low frequency non-separable transform (LFNST) index(LFNST_idx) syntax element for a current block of video data, the valuefor the LFNST_idx syntax element being non-zero and indicating asecondary transform for the current block of video data; determine thata multiple transform selection (MTS) scheme for the current block ofvideo data indicates a discrete cosine transform 2 (DCT-2) primarytransform for the current block of video data; and apply the DCT-2primary transform and the secondary transform during coding of residualdata for the current block of video data.
 7. The device of claim 6,wherein to determine that the MTS scheme for the current block of videodata indicates the DCT-2 primary transform for the current block ofvideo data, the one or more processors are configured to determine thatan MTS_idx syntax element has a value of zero.
 8. The device of claim 7,wherein to code the value for the LFNST_idx syntax element, the one ormore processors are configured to context-adaptive binary arithmeticcoding (CABAC) code the value for the LFNST_idx syntax element, andwherein the one or more processors are configured to determine a contextfor CABAC coding the value for the LFNST_idx syntax element withoutusing the value of the MTS_idx syntax element.
 9. The device of claim 6,wherein to code the value for the LFNST_idx syntax element, the one ormore processors are configured to decode the value for the LFNST_idxsyntax element; and wherein to apply the DCT-2 primary transform and thesecondary transform, the one or more processors are configured to: applythe secondary transform to decoded transform coefficients to produceintermediate transform coefficients; and apply the DCT-2 primarytransform to the intermediate transform coefficients to produce aresidual block for the current block of video data.
 10. The device ofclaim 6, further comprising a display configured to display decodedvideo data.
 11. The device of claim 6, wherein the device comprises oneor more of a camera, a computer, a mobile device, a broadcast receiverdevice, or a set-top box.
 12. A non-transitory computer-readable storagemedium having stored thereon instructions that, when executed, cause aprocessor to: code a value for a low frequency non-separable transform(LFNST) index (LFNST_idx) syntax element for a current block of videodata, the value for the LFNST_idx syntax element being non-zero andindicating a secondary transform for the current block of video data;determine that a multiple transform selection (MTS) scheme for thecurrent block of video data indicates a discrete cosine transform 2(DCT-2) primary transform for the current block of video data; and applythe DCT-2 primary transform and the secondary transform during coding ofresidual data for the current block of video data.
 13. Thenon-transitory computer-readable storage medium of claim 12, wherein theinstructions that cause the processor to determine that the MTS schemefor the current block of video data indicates the DCT-2 primarytransform for the current block of video data comprise instructions thatcause the processor to determine that an MTS_idx syntax element has avalue of zero.
 14. The non-transitory computer-readable storage mediumof claim 13, wherein the instructions that cause the processor to codethe value for the LFNST_idx syntax element comprise instructions thatcause the processor to context-adaptive binary arithmetic coding (CABAC)coding the value for the LFNST_idx syntax element, includinginstructions that cause the processor to determine a context for CABACcoding the value for the LFNST_idx syntax element without using thevalue of the MTS_idx syntax element.
 15. The non-transitorycomputer-readable storage medium of claim 12, wherein the instructionsthat cause the processor to code the value for the LFNST_idx syntaxelement comprise instructions that cause the processor to decode thevalue for the LFNST_idx syntax element; and wherein the instructionsthat cause the processor to apply the DCT-2 primary transform and thesecondary transform comprise instructions that cause the processor to:apply the secondary transform to decoded transform coefficients toproduce intermediate transform coefficients; and apply the DCT-2 primarytransform to the intermediate transform coefficients to produce aresidual block for the current block of video data.
 16. Thenon-transitory computer-readable storage medium of claim 12, wherein theinstructions that cause the processor to code the value for theLFNST_idx syntax element comprise instructions that cause the processorto encode the value for the LFNST_idx syntax element; and wherein theinstructions that cause the processor to apply the DCT-2 primarytransform and the secondary transform comprise instructions that causethe processor to: apply the DCT-2 primary transform to a residual blockfor the current block of video data to generate intermediate transformcoefficients; and apply the secondary transform to the intermediatetransform coefficients.
 17. A device for transforming a block of videodata, the device comprising: means for coding a value for a lowfrequency non-separable transform (LFNST) index (LFNST_idx) syntaxelement for a current block of video data, the value for the LFNST_idxsyntax element being non-zero and indicating a secondary transform forthe current block of video data; means for determining that a multipletransform selection (MTS) scheme for the current block of video dataindicates a discrete cosine transform 2 (DCT-2) primary transform forthe current block of video data; and means for applying the DCT-2primary transform and the secondary transform during coding of residualdata for the current block of video data.
 18. The device of claim 17,wherein the means for determining that the MTS scheme for the currentblock of video data indicates the DCT-2 primary transform for thecurrent block of video data comprises means for determining that anMTS_idx syntax element has a value of zero.
 19. The device of claim 17,wherein the means for coding the value for the LFNST_idx syntax elementcomprises means for decoding the value for the LFNST_idx syntax element;and wherein the means for applying the DCT-2 primary transform and thesecondary transform comprises: means for applying the secondarytransform to decoded transform coefficients to produce intermediatetransform coefficients; and means for applying the DCT-2 primarytransform to the intermediate transform coefficients to produce aresidual block for the current block of video data.
 20. The device ofclaim 17, wherein the means for coding the value for the LFNST_idxsyntax element comprises means for encoding the value for the LFNST_idxsyntax element; and wherein the means for applying the DCT-2 primarytransform and the secondary transform comprises: means for applying theDCT-2 primary transform to a residual block for the current block ofvideo data to generate intermediate transform coefficients; and meansfor applying the secondary transform to the intermediate transformcoefficients.